What are some possible reasons for this light to stay lit up on the dash? Possible fix to turn it off? 1994 Plymouth Voyager, 3.0

It does have ABS. You need a scan done on it to narrow it down. Could be a bad or dirty sensor, bad wheel bearing , wiring , fuse or controller. You could get a manual to help diagnos it.

What are some possible reasons for this light to stay lit up on the dash? Possible fix to turn it off? 1994 Plymouth Voyager, 3.0
Are we talking Air Bag or ABS here? I see both mentioned.

I have much the same problem with my ABS light. It comes on after I start moving, seemingly speed related. It comes on at about 35 MPH, and stays on then until I shut down. I have a '95 GC, 3.3 engine. It's annoying, but only knocks out the ABS portion of the braking system. The brakes still work well, simply without the antilock function. I'll work on it as time permits. I'm thinking probably sensors.

Sorry , you are right . His thread topic says ABS so I just assumed! Then he goes into air bag. My references were to anti lock brakes, sorry for the confusion.

The air bag light on usually means a faulty clockspring in the steering column.
Do a search and you will find many threads referring to this problem.