Drl does not come on

DLR module ???? DRL - daytime running lamps , doesn't have a DRL module. Why do you want to know that ? I see it coming , your going too replace it to see if it fixes the problem your having with the light's ? Without testing the circuit's . Do yourself a favor an take it to a qualified repair shop , before you make thing's worse .
Daytime Running Lamps (DRL)
The ambient light sensor is a light sensitive transistor that varies its signal to the body control module (BCM) in response to changes in the outside ambient light level. Any function or condition that turns ON the headlamps will cancel daytime running lamp (DRL) operation. With the headlamp switch in the OFF position, activating automatic lamp control (ALC), the front turn signal lamps will be turned ON after a 30-second delay under daylight conditions, which is determined by the ambient light sensor signal to the BCM. The DRL operates when the ignition switch is in the RUN position, the front wipers are not activated, and the transmission is not in PARK. When these conditions have been met and the ambient light sensor indicates daylight conditions, the BCM will illuminate the front turn signal lamps ON steady.
DTC B2645
Circuit Description
The body control module (BCM) monitors the daytime running lamps (DRL) ambient light sensor signal circuit in order to determine if the DRL or the headlamps should be turned ON in the automatic lamp control (ALC) mode. When the BCM senses the ambient light sensor voltage is between 1-4.9 volts, either the DRL or the headlamps will be commanded ON.
DTC B2645 Ambient Light Sensor Circuit

Behind the lower kick panel on the passenger's side good luck colin

That piece you think is a ceramic DRL module is a resistor , When in DRL mode voltage to the low beam headlamps circuit goes through that resistor dimming the headlamps from low beam to daytime running lamps . It sounds to me like you need a new resistor ,but without doing some electrical testing it could be a lot of things . The DRL relay in the under hood fuse box could have a problem , could be the BCM - body control module , the ambient light sensor etc... Here is how daytime running lamps work .
Daytime Running Lamps (DRL)
The ambient light sensor is a light sensitive transistor that varies its voltage signal to the body control module (BCM) in response to changes to the outside (ambient) light level. When the BCM receives this signal it will either turn on the daytime running lights (DRL) or the headlights. Any function or condition that turns on the headlights will cancel the daytime running lamps operation. With the headlight switch in the OFF position, the headlights will either be turned ON or OFF, after an approximate 30 second delay depending on whether daylight or low light conditions are sensed. The HTR A/C IGN fuse in the underhood junction block supplies ignition positive voltage to the daytime running lamp (DRL) relay coil circuit. The DRL relay switch contacts are connected to the low beam circuit. When the headlamp switch is placed in the OFF position, the BCM will either turn on or off the daytime running lamps, depending on whether daylight or low light conditions are sensed. The BCM energizes the DRL relay, closing the switch contacts and grounding the low beam circuit. Ground is provided at G101. The DRL illuminate the low beam headlights at a reduced intensity. The DRL will operate when the ignition switch is in the ON position, the gear selector is not in the PARK position and the parking brake is released. When these conditions have been met and the ambient light sensor indicates daytime conditions, the DRL will illuminate.

No on the fuse . The LH HDLP and RH HDLP fuse in the fuse block - under hood, supply battery positive voltage to both low and high beam lamps at all times. For manual operation, when the headlamp switch is in the ON position, the headlamp switch supplies ground directly to the headlamps and to the body control module (BCM) on the headlamp low or high beam signal circuit, depending on the position of the headlamp dimmer switch. The BCM uses this signal to determine if the conditions are present to illuminate the daytime running lamps or park lamps.
The headlamps may be turned on 2 different ways. First, when the driver places the headlamp switch in the ON position, for manual operation. Second, with the headlamp switch placed in the OFF position activating automatic lamp control (ALC).For ALC operation, the BCM receives a signal from the ambient light sensor indicating a low or high ambient, outside, light level. Under low light conditions the BCM grounds the headlamp relay control circuit energizing the headlamp control relay. The now closed relay supplies ground through the headlamp switch to the headlamps and the BCM on the headlamp low or high beam signal circuit, depending on the position of the headlamp dimmer switch. When the BCM grounds the headlamp relay control circuit it also grounds the park lamp relay control circuit illuminating the park lamps. The headlamp relay is grounded at G203.
Daytime Running Lamps (DRL)
The low beam headlamps operate at reduced intensity when in daytime running lamps (DRL) mode. The ground circuit to the switch side of the DRL relay has a resistor in-line to reduce the intensity of the low beam headlamps for DRL operation. The body control module (BCM) receives a signal from the ambient light sensor indicating a low or high ambient, outside, light level. Under daylight conditions the BCM grounds the DRL relay control circuit energizing the DRL control relay. The now closed relay supplies ground directly to the low beam headlamps and to the BCM on the headlamp low beam signal circuit. The low beam headlamps now illuminate with reduced intensity. The DRL relay is grounded at G203. Any time the headlamps are illuminated the DRL will not illuminate. Manual park lamps do not effect DRL operation.

It is located in the underhood fuse/relay box , marked DRL 10 amp fuse ! Also if that is good check the DRL relay in the same fuse/relay box .Your light sensor could also be bad .
The daytime running lamps (DRL) will operate when the ignition switch is in the RUN position, for automatic transmissions (A/T), the gear selector is not in the PARK position, the headlamp switch is in the AUTO position, and for manual transmissions (M/T), the park brake is released. When these conditions have been met and the ambient light sensor indicates daytime conditions, the DRL will illuminate. The ambient light sensor is a light sensitive transistor that varies its voltage signal to the body control module (BCM) in response to changes to the outside (ambient) light level. When the BCM receives this signal it will either turn on the DRL or the headlamps for auto headlamp operation. Any function or condition that turns on the headlights will cancel the daytime running lamps operation. The DRL can be manually turned OFF by depressing the AHL/DRL switch in the headlamp switch
Do you know that on inside of fuse box lid it shows what fuse is what .

Daytime Running Lamps
With the daytime running lamps (DRL) programmed to be on, the DRL will operate when the ignition switch is in the ON position, the gear selector lever is out of the PARK position, the headlamp switch is in the OFF or PARK position, and the ambient light sensor indicates daytime conditions. Battery positive voltage (B+) is supplied to the DRL relay coil through the underhood fuse block. Battery positive voltage is supplied through the underhood fuse block FOG/DRL Fuse to the DRL relay normally open contact. The DRL relay normally closed contact receives ground for normal high headlamp operation. When the dash integration module (DIM) determines that conditions are right for the DRL, the DIM grounds the DRL relay coil. This energizes the DRL relay coil and closes the switch to the normally open contact. Battery positive voltage (B+) is supplied to the LH and RH high beam headlamps in series. The high beam headlamps split the voltage and each lights at half intensity. Current will follow the path from the DRL relay to the LH high beam headlamp, HDHIBML Fuse, HDHIBMR Fuse, the RH high beam headlamp, then to ground.
Does your vehicle have
Twilight Sentinel
The twilight delay switch in the headlamp switch is supplied a reference voltage from the instrument panel integration module (IPM). It is supplied a reference ground from the IPM. The switch is a potentiometer that resistance varies as the switch is moved. The IPM receives an input voltage proportional to the resistance of the potentiometer. The IPM sends a class 2 message to the dash integration module (DIM) indicating the on/off status and delay length for the twilight sentinel. With the twilight sentinel in an ON position, the DIM will automatically control the headlamps on/off status depending on the nighttime/daytime status of the ambient light sensor. The DIM will use the twilight sentinel delay length to know how long to keep the headlamps and park lamps on after the ignition switch transitions from ON to OFF during nighttime conditions.
If you don't know about these things you best bet is to take it to an ASE certified repair shop or the dealer .
If you
Your best

There is no DRL relay , has a lamp control module .
The daytime running lamps (DRL) activate under the following conditions:
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The ignition switch is in the RUN position.

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The ambient light sensor indicates daylight.

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The vehicle is not in the PARK position.

When the above conditions are met, the lamp control module (LCM) supplies battery positive voltage (B+) to the low beam headlamps through CKT 589 (GRY), the DRL resistor, and CKT 12 (TAN). The DRL resistor reduces the voltage supplied by the LCM. The low beam headlamps light at a reduced intensity. The DRL disable if the vehicle is placed in the PARK position. When the ambient light sensor indicates darkness, the low beam headlamps automatically switch from a reduced intensity to a regular intensity.
Lamp Control Module (LCM)
In the center of the IP, below the center heater outlets

Without testing i would say you have DRL control module problem , But that would just be a guess .
In the night mode, the DRL ambient light sensor senses darkness. Then, the DRL module turns off the front turn lamps and turns on the headlamps through circuit 10. The DRL module also turns on the park, side marker, license, and tail lamps. If the engine should stall with the DRL control module in the night mode, the DRL control module will turn off the headlamps and leave the side marker, park, license and tail lamps on while the engine is being cranked. The headlamp switch operates as usual.
The Daytime Running Lamps (DRL) control module is designed to automatically operate exterior lights depending on outside light conditions. The DRL control module operates in two modes, the day mode and the night mode. In the day mode, the DRL ambient light sensor senses daylight. Then, the DRL control module turns on the front turn lamps (non-flashing) if under the following conditions:
• The ignition switch is on.
• The headlamps switch is in the OFF position.
• The park brake is released.

The brightness of the Vacuum Fluorescent (VF) displays is controlled by two signals: the park lamps on signal (circuit 230) and the VF dimming signal (circuit 308). With the park lamps on, the VF display of the radio, heater, A/C control (with RPO CJ2) and the instrument cluster will dim for nighttime viewing. When the park lamps on signal is not present (park lamps off), the VF displays are at high brightness for daytime viewing. When the park lamps are on, the I/P lamp dimmer switch provides a signal (VF Dimming Signal circuit 308) which controls the brightness of the VF displays when the I/P lamp dimmer switch is adjusted.

Do the Daytime running light's work ?

check the drl 9daytime running lights0 relay under the hood. I could be stuck in the on position.

Yes. These are called DRL's or daytime running lights. It is law that vehicles manufactured after 1985 must have low amperage lighting on while running.