Why would the 'air bag' light in your 1998 Dodge Caravan stay on all the time?
There is a "clockspring" in the steering column that is probably broken. When the clockspring breaks, the airbag light comes on. The "clockspring" takes the place of the old slip rings and spring loaded contacts used in older cars to transfer circuits from the steering wheel to the stationary column making the airbag, horn and speed control operational. To replace involves removing the airbag. Take it to the dealer. This was a recall but was not made public, i had the same problem and the dealer fixed it for free. The airbag light came on in my 1994 Caravan and I found the clockspring answer. But when the clockspring is bad, the horn won't work and my horn did work. I called the dealer's service dept and got the clockspring answer. I said it's not that because the horn works. I was told to bring it in for an $80 diagnostic test. Instead, I went back to the manuals and checked the fuse information. Fuse #13 showed the air bag and the rear wiper together. My rear wiper wasn't working, so I replaced fuse #13 and that fixed the problem!
It could be several things. The fuse, clock spring, connection at the air bag harness, bad ground wire. If it is the air bag connection you are going to check make sure to disconnect the negative batter cable to avoid accidentally triggering the bag and causing serious injury to yourself. If you need to change the fuse (although not stated or totally necessary) for the air bag i would also disconnect the battery cable just to be safe. Hope all this info helps to find your problem. Good luck with it. You can also use a code reader to reset the code and see if it stays off.