Originally Posted by
DenverGP
I repaired a friends Dodge neon that had similar sounding electrical issues. The turn signal assembly (they call it the "multifunction switch") in the steering column has a lot of different circuits running thru it including headlights and hi-beams, and the wiring/connectors can't handle the amount of current. The electrical connector was melted pretty bad, causing a short circuit. When I went to a junk yard to try to get a replacement, out of 4 cars in the junkyard with the matching part, all of them had melted connectors (but apparently not bad enough to cause the short yet).
I've seen reports that other dodge models besides the neon had the same issue, so the multifunction switch assembly would be my first bet.
In my friends case, it got even worse because it blew a fuse, so they replaced the 5 amp fuse with a 25 amp. That caused the main wiring harness in the steering colum to melt, shorting out all sorts of fun stuff.