Weird potentially dangerous electrical problems

As the title suggests, I am having some rather odd problems. Its my girlfriends 1995 V6 Mustang. I'm not new to working on cars, but new to a problem like this.

A couple weeks ago on our way home from an outing, the headlights started to flicker. Closer to home and they eventually started going out. If one pulled the headlight switch out, or even hit the dash hard enough, they would come back on. Neither high nor low beams would work, but the running lights would, similar to if you only had the switch pulled back one notch. Also if it happened while running with the high beams on, the high beam indicator would go out. This problem has now gotten to the point of it happening every time we drive out at night. But everytime enough jiggling of the switch persuades them to come back on. Also, on a side note, I have noticed every now and again, the voltmeter takes a dive really quick and pops back up. But, that has not happened in conjunction with the headlight problem.

I know there is a search function, but there are a lot of threads to read through, so I apologize if this has been covered to often. If there is a thread that explains this, please by all means, link me up.

Also, the car does not have factory fogs. I've been reading that those are a cause for some cars, but hers hasn't ever had fog lights.

I'll go check that out. I had the dash of my 98 apart before, so I know how to get into it. Where is that located? Right behind the switch?

Okay, I replaced the switch. I spliced all the new wires in and the switch works like it should. The lights still randomly shut off though. Would the headlight relay be shutting them off still?