[84LX89GT]

Have you checked the grounds. Having a ground problem will cause all sorts of weird stuff to happen like you described. what kind of referance material do you have for wiring diagrams?
Another thing you may want to look at is your multifunction switch. Ford routes alot of circuits through that switch (parknig lights, head lights, turn signals, etc.)
Another thing mustangs are notorious for is bad harness bulkhead connectors and you may have an intermittent open/short in one of those wires especially since they tend to vibrate and rub together. The only way to isolate it is really to pinpoint it to a certain circuit and section of wire.
I've been looking through my Chilton's book (which sucks BAD!) and it looks like alot of the main light circuitry goes through that switch and since the manual doesn't show interior lighting i don't know if the multifunction switch is in any of that circuit (dash lighting), but it may carry an essential ground....i'll try and look up some more if i get an opportunity. Keep us posted!