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.