No high beams - 2002 Buick LeSabre

Bright lights wont shut off ? Assume you mean high beams ? Reading how they work might thing high beam relay has stuck contacts inside .

Headlamps
The headlamps may be turned ON 2 different ways. First, when the driver places the headlamp switch in the HEADLAMP position, for normal operation. Second, with the headlamp switch placed in the AUTO position, for automatic lamp control (ALC). During ALC, the headlamps will be OFF in daylight conditions, or low beam operation in low light conditions. Battery positive voltage is supplied to the low beam relay and the high beam relay in the underhood fuse block. When low beam headlamps are requested, the body control module (BCM) supplies ground to the coil side of the low beam relay. This activates the relay and the relay supplies voltage to the left hand low beam headlamp through the LH LOW BEAM fuse and to the right hand low beam headlamp through the RH LOW BEAM fuse. Ground for the left hand low beam headlamp is provided at G101. Ground for the right hand low beam headlamp is provided at G102. When high beam headlamps are requested, the body control module (BCM) supplies ground to the coil side of the high beam relay. This activates the relay and the relay supplies voltage to the left hand high beam headlamp through the LH HIGH BEAM fuse and to the right hand high beam headlamp through the RH HIGH BEAM fuse. Ground for the left hand high beam headlamp is provided at G101. Ground for the right hand high beam headlamp is provided at G102.

It could be driving lights mode instead of low beam. Check connections.

back for high beam forward for low beam
high beam will not work in low beam position

High Beam Headlamp Operation
Battery voltage is applied at all times to the coil and switch sides of the HIGH BEAM PCB Relay located in the underhood fuse block. When the headlamp dimmer switch is placed in the high beam position, the headlamp dimmer switch signal circuit to the BCM is pulled low signaling the headlamp high beam request. In response to this signal, the BCM applies ground through the high beam relay control circuit energizing the high beam relay. With the high beam relay energized, battery voltage is applied through the switch side of the relay, the left and right high beam fuses, and the high beam supply voltage circuits illuminating the high beam headlamps. At the same time the BCM sends a GMLAN serial data message to the instrument panel cluster (IPC) requesting the IPC to illuminate the high beam indicator. Ground for the left headlamp is provided at G101 and the right headlamp at G100.

That should be the problem.
Check the voltage at the dimmer on each setting.

the high beam switch is at fault
A new one is needed
The directional lever you pull up on to switch to high and low connects to a rod which is going to the high beam switch at the mid section of the steering coluum. It is a headache to change for your on your head replacing this part

DID YOU CHECK THE BULBS?

high beam switch is faulty look at getting a new stalk.....

probably the connections on the lever/arm .

replace the switc and also ck the hi beam relay