The above and more. If you seem to have the original wiring, start by reading this excellent article, which even if you don't do this mod. It accurately describes typical problems caused by age and corrosion, adding more "stuff" to the system
http://www.madelectrical.com/electricaltech/amp-gauges.shtml
Your suspects in 'approximate' order are:
Deteriorated connections in the bulkhead connector and ammeter circuit
As mentioned, bad headlight switch or switch connector
Maybe not "now" but bad dimmer switch and connector
Certainly the lighting connections and charging / battery terminals in the bulkhead connector, already mentioned
GROUNDS at the headlights
Headlight connectors
As mentioned, voltage regulator problems
In addition, greasy, dirty, worn alternator brushes and connections to them
The THING is you could very well have multiple problems.
Not knowing the history of your car (humidity, leaks, rust, corrosion in part) hard to guess.
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Where to start?
Treat "the problem" as if it's ONE problem, and identify and fix "that" problem. If that turns out NOT to be the total fix, start over again
EG: Part of problem with the dash lighting might be
I would start by measuring interior voltage at some point, while experimenting with the light switch. Find the main wire supplying the fuse panel and monitor that with a voltmeter. Turn the lights on/ off and see what happens to voltage there That might give you a clue as to "is it voltage drop?"
If not.....might be lighting feed wires going through the bulkhead connector
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On a different track, monitor charging voltage while running at "low cruise" RPM. Post what you have there, warmed up. Should be close to 14V. Much above 14 and certainly above 14.5 is too much or at least "heading there."
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I would actually inspect the light switch connections. You will have to remove the switch. With lights on, wiggle up in there around the switch and harness and look for dimming and flickering
Disconnect the bulkhead connector out in the engine bay and inspect.
Also, if you don't have, get a reprint shop manual. Factory manual. You can find these on ebay and "around" the internet. You can ALSO download FREE shop manuals at MyMopar:
http://www.mymopar.com/index.php?pid=31