I have had a few dodge trucks over the years and have never ran into a problem like this before. My step son bought a 1999 Dakota 3.9 five speed 4x4 it had a few problems when he got it one being the blower motor didn’t work at all. The previous owner installed a toggle switch to run it on high that didnt work at all the time. So I figured it was the resistor I pulled the dash checked it it was fine, I pulled the motor and it ran off the battery I had 12 volts at the wire running to the fam motor. So I bought both a resistor and a motor which didn’t fix nothing. I was trying to get a ground for my tester and while losing the nut for the ground under the dash ( on the passenger side kick panel) my wrench touched the dash the motor started to run I unhooked the new one hooked up the old one and the old resistor and it works as long as you ground the metal of the dash to the ground on the under the kick panel. Have know ideal why but it works as it should.

 

It's possible a wire smewhere is either broken or has a bad connection. You can run a ground wire to chassis amd see what happens.
Evidently you have a ground problem.

 

I bet there's other things not working that you haven't noticed....I've never had one of these dashes apart, but I bet PO replaced the heater core or something and missed a strap and didn't feel like digging it all open again.

 

the grounds for the dash are very important its the two nuts on the bottom of the complete dash on both sides check to see if they are good and tight. I think both sides have ground wires attached on these studs be sure they are attached.

 

on either side inside cab down by your feet are kick panels pull these off behind them you will see were the complete dash bolts down if these are loose you will have either no ground or intermittent ground.