The "ceiling light things" are accumulators. They have a pin in the middle, sticking out of a rubber grommet. Is this what you mean? If one of the pins has extended, this is not really a problem. I've never heard an explanation for the pins changing state, or affecting anything, but it doesn't seem to affect anything at all. Try pushing it back in. I think it will.
Here's what I would do:
Turn the key to RUN. Do the BRAKE and ANTILOCK lights both come on for 2 seconds and go out? If = NO, something is wrong. Begin with the battery connection wiring. If = YES:
Jumper A and H (top row far right is A, bottom row second from left is H) in the ALDL. Turn key to RUN. The ANTILOCK light will flash the codes. The "normal" all-is-well code is 14. (If you see code 12, you have a 4X4 or 2WD BPMV). (If you see Code 15, your foot is on the brake pedal).
If there are other codes, write them down. Then clear them. Remove jumper. Turn key to RUN. Jumper A and H for two seconds, remove for one second, jumper for two seconds, remove for one second, repeat. When ANTILOCK and BRAKE lights come on, then go off the code-clear was successful. Learning to clear the codes is fussy. Turn key OFF, wait about 10 seconds, then turn key ON and try again. You'll eventually get it.
Recheck for any codes. If there are still codes, it is a current code. Usually a wheel sensor code, and will be the sensor or wiring. Wheel sensor resistance is 1,000-2,000 Ohms. IIRC, typically 1,700-ish.
When you're code-free (only 14 remains), go for a drive. At 8 MPH-ish you should hear a "grrrr" of the motor doing its self-test. Another test I sometimes try: After first start, ride the brake pedal a little, and accelerate gently to 15+ MPH. The ANTILOCK light should come on at 15 MPH. Stay above 15 MPH and release the brake pedal. ANTILOCK light should go out. (If you ever find Code 86, it is from this happening too many times. 86 will always clear if the brake pedal switch is adjusted correctly).
There's some ideas.
Will I have to program anything if it comes from anything else?
There may be a way to flash these, but it is specialized equipment, dealer-only shit, that they probably can't find anymore because they haven't used it for 20 years, and some tech took it home... The best way to deal with a replacement module is to either transfer your electronics module, or power it up and watch for certain codes. And the easiest is to obtain a 91-92 4-sensor module, and jumper pin D in the 10-pin connector to ground, which puts the module in 4WD mode at all times, so it will behave very similarly to the AWD program.