now i could be wrong but many mopars allow you to switch on the interior light by turning the headlamp switch as far anticlockwise as possible. i.e brightest setting for dash lights and 1 click more
the light will work with the ignition on and off
any other curtesy lights are on the same circuit.
the dome light is set into the roof.
the back of it should not press on the inside of the metal roof but it probably will...however chrysler had a few ways of ensuring it didn't short out .  some have a back on them  others just have a bit of fiber board/cardbord that was orginally glued to the roof or the back of the light/  haven't established which
either way afetr 30 or 40 years of condensation it can come off and move about exposing the spade connectors at the ends of the light fitting to the inside of the metal roof.
my cars battery used to go flat and occaisionally i would get the smell of burning plastic.
because my light didn't work i had no idea that the feature on the headlight switch existed so my interior light was powerd up all the time and occasionally shorted out somewhere in the roof  heating up the wire all the way back to the junction behind the kick panel.
it never got hot enough to go on fire and it never really sparked or arced because the headlamp switch was so corrded and kanckerd that it didn't allow much current to flow.
i re stuck the fibreboard
fitted a headlamp switch out of a jeep  (its the same and you can change the knob for yours)
job done.
check it by switching the light on by either opening a door or using the dash headlanp switch.
put meter on volts DC range
stick the black lead into any clean body metalwork junction you can (i usually wedge mine under the edge of the alluminium sill trim plate)
and stick the red lead on one end or t'other of the bulb one end should read 12 volts. if you get nothing try black lead to one end and red to the other. if you get - 12 then the black in on the power end and the red is on the return lead   (which will earth to the body at one of the door jam interior light buttons, continuity test it with ya beeper if you want).
next issue was the 4 pin connector from the ignition switch.  it had corroded in a way that on damp mornings the car would start but on dry mornings it wouldn't  electric supply was erratic for all circuits and i was getting only 8-9 volts on the leads into the fuse box,
that connector was cut off and was replaced by using plastic coated screw connectors choccy block stuff for cooker rated wireing
next the car started refusing to do anything. usually on a saturday half way round shepherds bush roundabout.
this was caused by the collpase of the ingition lock switch. that was rebuilt using the springs out of a front door yale lock  
 
other fun i have had
bulkhead connectors stopped headlamps horn working
all pins cleaned bent slightly and sprayed with wd40
none of my lights earthed properly so 1 set of indicators worked normally one set blinked apprx 3 times a minute
my fuse box was so corroded i had 12 volts at the feed side and anything from 0m -5 volts at the other end of the fuse.  that sat in a bucket of coke for 3 weeks  and then got a pollish up with brasso wadding wrapped round a rubber tipped dremmel bit.
put the fuses back in and sprayed the whole thing with PCB board varnish. looks a bit crappy but hasn't been an issue since
the earth strap to my engine was bolted on to an additional bolt at the engine mount which was loose so i had intermittent good and bad running of my points ignition  (new strap new bolt spiky washer and junked the points) 
the rear lights didn't work because the numberplate light shorted out to the bumper but the bumper mounts were so rusty it again saved the plastic on the loom burning up.
none of the dash lights worked cos it wasn't screwed down
the brake warning light had been taped over to hide the fact that the master cylinder was in emergency 1 circuit mode....i had no back brakes
now all of this really caused me a lot of frustration and annoyance cos the car in general is pretty good.
i ended up working from the battery to the fuse box via the ignition switch with a volt meter   to check i got 12v between the wire i was testing and the body.  once i was happy with the feed to the fuses the same was done from each metal cap end of each fuse and then each spade connector for each fuse
I then followed each non working circuit until i got to the non functioning thing. (this highlighted my bulkhead connector issues as everything up front goes through there
next i used the beep beep continuity tester on the multimeter to check my switches actually switched something
1 pin switches check continuity between the body of the switch and the  spade  (some light switches)
2 pin switches hard to tell some of them work by connecting a live circuit to eath to complete the circuit i.e the switch is after the ancilliary that needs powerd 
ignition switch  you will have 1 feed wire  (thick)
2 (ornage a blue i think) wires that feed general circuits and ignition circuit power to the fuse box
and a thin one that goes off to the solenoid that controles the starter.
its probably best just to voltage check each at different positions.
anyway its a pain in the butt
but worthwhile as i haven't (touch wood) had any issues
but you need the wireing diagram for your car to establish which wires carry power and which wait until a switch is switched to carry power.
eg the brake lights circuit. the bulbs holders are powered up but the light doesn't light until the circuit is completed by the switch earthing. its bolted to the brake peddle bracket.
anyway if the wires  are still good but its just the connectors don't worry it can be sorted
if the wires have all been replaced with grey door bell wire and no lables worry
you are not alone in your quest for good eletrics
dave