It would be unbelieveably handy if you would post what year/ model you are working on
Dash lights has nothing to do with the dash limiter
Rear stop/ tail lamps normally has nothing to do with the bulkhead connector, unless there's a short up front,
Some issues with the dash:
The connector pins where the harness connects to the PC board(s) is subject to loose pins or corrosion, or even broken pins
The boards get corroded in many ways including.......
Where the harness connects
where the temp/ fuel gauge studs/ nuts connect
where the screws connect to the dash casting
corrosion where the lamp sockets fit
corrosion where the voltage limiter fits, and the springy fingers that form the "socket" lose connection to the PC board.
Your problem sounds more like a damaged/ melted/ rusted headlight switch connector.
Frankly, I'd pull the switch, the dash, and inspect them both, as well as the fuse box connectors.
Easy, and not that time consuming, take a Sat. afternoon.
You have a shop manual? You can download one for free
http://www.forabodiesonly.com/mopar/showthread.php?t=132309&highlight=click+save
Pull the bolts out of the column floor flange, pull the trim under the column, and there's a bolt up in there up near the brake linkage. Then two more nuts on studs that hold the colum up. Remove these and the column should drop down into the seat.
Now find/ feel the speedo drive and remove the cable, and remove the battery ground. Pull the screws and remove the dash cluster.
Headlight switch is a trick. Turn the switch ON, then reach up around the switch and feel for a mechanical button. when you push it, the knob and stem of the switch will come out of the switch.
DO NOT TRY and remove the knob from the stem.
A photo of a generic switch:
