Green light little green light shaped like a sun with "rays" is on. It is by the temperature gauge and oil indicator on the dash. We just noticed it on and maybe it has always been on but we cant remember, Our truck is new to us but we have no manual.

https://www.dash-lights.com/chevrolet/malibu-dashboard-warning-lights/

Replacing a fuel pump has nothing to do with instrument cluster lights or the clock staying on. Unless you shorted wires , did you disconnect the negative battery cable before hand ?
The body control module (BCM) performs the following functions:
• A/C compressor request
• A/C cooling fan
• Exterior and interior lighting control
- Daytime running lights (DRL)
- Automatic lighting control
- Fog lamps
- Interior lighting
• Battery rundown
• Chime
• Gauge control
• Instrument cluster indicator control
• Fuel gauge control
• Temperature gauge control
• Theft deterrent
Interpreting all of the driver warnings sent by the control modules on the class 2 serial data line
Sending the information to the instrument cluster in the form of a SPI serial data bus message
The following list of messages are sent by the BCM to the instrument cluster:
• Fuel gauge position
• Temperature gauge position
• Oil pressure
• Low engine coolant
• Check oil
• Volts
• ABS
• High beam
• Low fuel
• High temperature
• Washer fluid level low
• CRUISE
• BRAKE
• SERVICE VEHICLE SOON
• Door ajar
• Seat belt
• THEFT SYSTEM
• PRNDL
Check the fuel level sensor wires , the fuel level sensor is a input to the BCM .

Oil pressure sensor, or most likely, oil level sensor, either sensors, wires, or connections.

The red square shaped warning dash light is an image of a crudely drawn radiator indicating that you are low on coolant. Topping up your coolant bottle reservoir located on the passenger side above the wheel should clear up your issue. If your coolant level is full and is still indicating low coolant via dash warning light, you could possibly have a sensor out in the radiator or air bubbles in your coolant lines that need to be bled out.

instructions:

1 Turn the ignition key to the "II" position.

2 Check the lights on the dash. You should see a variety of dash lights light up. One of those lights will be a "Check engine" light. This light should stay lit with the ignition key in the "II" position. The rest of the lights should go out. If the "Check engine" light begins to blink, you may have a problem with one of the vehicle's electronic components. Consult your owner's manual or call your dealership for possible servicing issues.

3 Start the engine. The "check engine" light should go out after a few seconds. If it does not, this can indicate either a maintenance interval has been reached or a more serious problem with the vehicle's emissions control system. Again, it is advised to consult your owner's manual or call the dealership for service.

4 Check for an illuminated "SRS" light on the dash. The SRS light indicates a problem with the supplemental restraint system, i.e., the airbag, on the Camry. This needs to be serviced by a professional mechanic.

5 Check for an oil light on the dash. The oil light is in the shape of a small oil canister. When this lights up, it indicates low oil pressure. Low oil pressure is caused by a blockage in the system, a weak oil pickup or oil pump, or low oil levels in the engine. Check and see if your Camry is overdue for an oil change. It is recommended that the oil be changed at 5,000 miles or every six months.

6 Check for the low fuel warning. The fuel light on the Camry is on the fuel gauge near the "E" on the gauge face. The low fuel light means that you have to refuel your vehicle.

7 Check for the seat belt warning light. The seat belt warning light is a picture of a figure wearing a seat belt. If your seat belt is unbuckled, then this light will illuminate (along with a warning chime) indicating that you should buckle up.

8 Check for an orange car with lights on (on the dash lights). This warning light indicates that one or both of your brake lights has failed, or the electrical resistance in the bulb filament indicates that it is about to fail and will need service soon.

BMW PARTS

you should switch the temperature sensor and oil pressure sensor you had on your first engine,because your new engine must come with the light indicator dashboard so the sensor of your new engine are not compatible with your gauges....lipak!...

ck the engine to body ground.located back side of engine and srew to firewall.

This could be two unassociated problems; the flickering oil light can indicate that the pressure sensor for the idiot light is failing- this is not uncommon, the other can be a failed temperature sensor sensor on the main radiator. 
The low oil pressure condition may also be indicative of a worn engine part or parts. It would make sense to have the actual oil pressure checked in a shop to see if it is in the normal range which should lay between ~30 & 60 pounds depending on engine RPMs and engine temperature. The idiot lights trigger at around 4-5 pounds and this is really pretty late for a warning; if the pressure is actually that low, not only lubrication is too little but the cooling effect of the circulating oil is inadequate.
If it was my car, I would replace both sensors before getting too worried. The cost of these together (parts only) should be well under $50 US.  

HEY,
YOU SEEM TO BE ON THE RIGHT TRACK. I WOULD START WITH THE SENDING UNITS. GM LOVES TO PUT TWO OF THE ON A CAR. ONE FOR THE GUAGE AND ONE FOR THE DASH LIGHT. UNLESS YOU HAVE NOTICED ANY BIG CHANGES IN OIL PRESSURE I WOULD THINK IT IS THE SENDER(SWITCH) FOR THE LIGHT. THEY ARE NORMALLY LOCATED AROUND THE AREA OF THE OIL FILTER HOUSING.

I believe that's the low beam headlight indicator. The circle w/ lines going to on side is the highbeam indicator. You can download your owners manual from Toyota.