When the headlights are turned on the fuel and oil pressure gauges quit working. When the headlights are turned off the gauges begin working and return to normal operation. What could cause this?

That is a strange one. With park lights or just headlights. I'd start by reaching up & wiggling the headlight sw & see if anything happens & check for loose connections in that vicinity.

What happens when you just turn on the parking lights? Have you tried tightening the screws holding the instrument cluster in? It sounds like a possible ground problem with the dsah lights.

Thanks Robert....

With your help & suggestion I may have solved the problem. The problem with the gauges occurred in both the park and headlights on position. I remembered that I left the connector loose on the back of the dimmer/dome light switch because I've been taking the connector off to test and attempt to solve a problem with my dome light not working when operating the thumb wheel switch on the dash. I left it somewhat loose so I could get it off easily to do some testing. I did like you said and pushed it on all the way and it appears that that solved the problem even though I don't see a connection between the dash light dimmer/dome light switch and the gauges. But again, a big MOPAR thanks to ya!

Jim