On one of my Chrysler products (a 1970 C-body), I was "lucky" to acquire one that had the Rim Blow horn in the steering wheel. I bought the car in 1975. When they were new, that feature was touted as a safety feature as you only had to squeeze the wheel to get the horn to blow, instead of pounding on places that might make the horn work on the steering wheel.
As delivered, it worked most of the time. When the temp was above about 80 degrees and the car was in the sun with the windows rolled up, the horn would activate by itself. The fix was to unplug the horn relay. What I found when the horn ceased to work (and took the cover off the relay) was a severely cooked relay. There was much oily gook inside from the insulation of the wire windings that made it all work. A new relay got things working again, until there was something that made the Rim Blow toot it's own horn again. I also went in search of a steering wheel that had a regular horn setup in it too.
The instrument panel items sound like a poor ground issue. On the Chryslers that share that general instrument panel design, there are a few hidden ground straps in the floodlight lighting for the instrument panel gauge area, which you can see if you look at that area from the floor area looking upward. One of two Phillips head screws that hold the plastic panels together contact with them. Not sure if that might help the problems you have, though.
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