one place to look very carefully at, no matter the age [or mileage] is the connection at the bottom of the steering column.
i have seen, and repaired, MANY of those connectors because they get hot and melt.
dodge, chrysler, or plymouth, it doesn't seem to matter. for some reason, [and i suspect vibration as the instigator] the earlier models with just the turn signal switch and horn, are not too bad for this, but it still happens.
however, when the key went into the column, those connections really started to show "meltyness" problems.
hopefully, the OP's connection is good there. if so, it still should be taken apart and the crimps should be checked for tightness as well as the male and female pins fitting together tightly.
after that inspection, with all being good, add a dab of die-electric grease to the connections before plugging them together.

one place to look very carefully at, no matter the age [or mileage] is the connection at the bottom of the steering column.
i have seen, and repaired, MANY of those connectors because they get hot and melt.
dodge, chrysler, or plymouth, it doesn't seem to matter. for some reason, [and i suspect vibration as the instigator] the earlier models with just the turn signal switch and horn, are not too bad for this, but it still happens.
however, when the key went into the column, those connections really started to show "meltyness" problems.
hopefully, the OP's connection is good there. if so, it still should be taken apart and the crimps should be checked for tightness as well as the male and female pins fitting together tightly.
after that inspection, with all being good, add a dab of die-electric grease to the connections before plugging them together.

Agreed, I'll be sure to look over the steering connector with heightened concern, good suggestion.

those are called "MOLLEX" connectors if i remember right.
the two sizes used are .093 and .125, again if i remember correctly.
the kits can be bought in several places, as well as the individual items.
i make sure i have all of the items needed on hand because this is such a common problem.
one thing to make DAM sure of when replacing each of the connectors. when you are done with your crimp, look at the mating surfaces and be SURE they are ROUND.
if they are not, just the sides of the terminals will touch, which means the current flow is only through two VERY THIN contact points. resistance is up, heat is caused, and we all know what happens next.
i can't stress this enough. it is especially critical on the female side, and when you push the connectors together, make SURE you push them together STRAIGHT.
if you fight them, there is a very good chance one or more of the female terminals will get egg shaped.
this is probably one of the reasons the newer stuff went to those tiny spade type with the flap on the female side, to ensure a tight connection at the column.