Hey,
Thanks for posting this problem. I just recently purchased a '99 XJ Classic and started to have these problems around (1400000kms). My first problem was my cruise control that was acting up, where the sensor needed to be replaced (If I can remember correctly).
After that repair, I started to have the exact same problem that you are describing. Whenever I drive over traintracks or just sometimes driving down the road my airbag light will come on and only my tach and sped will drop down as if the jeep is turned off.
I brought it into the dealership (5 Star Chrysler) and I really don't think they knew WHAT was going on and were claiming that it was best for me to deal with it as if I were to get it fixed it would cost over a grand easily.
Needless to say, It's been a couple weeks now and I've put up with it. As long as it isn't affecting my airbags then I am feeling good. I will try turning my right blinker if that happens next time.
NOTE: I thought it was an entire electrical problem as my front driver and passenger speakers have recently stopped working and my passenger side and rear window switches have stopped working.
I'm wondering are you have any of the same issues or have had them in the past?