I replaced the wiper motor and harness, new reverse light switch on the trans, new reverse light harness... Exterior reverse lights work as they should. The reverse light on the dash is on all the time, not just in reverse. Any suggestions? Car is a 70 road runner 4 speed.

what about the back up lamps on rear?

Is the switch the right one? Mopar had switches of various lengths I do believe.

It's just a light bulb connected to the switch you replaced on the transmission. The two black wires that go to the switch connect next to each other at the bulkhead disconnect & go to the light (power comes in somewhere...see wiring diagram).

1. Disconnect the plug at the transmission switch with the transmission NOT in reverse.
a. Light goes off, bad switch
b. Light stays on, a short somewhere.

2. The next place I'd look is at the bulkhead disconnect since you were just messing with the wiper motor wires. Are they plugged in correctly? To the correct connection (or backwards)?

3. Lastly, start following the wires looking for a short.
a. Did the two black wires going to the trans get melted on a header?
b. Something under the dash touching/melted together?

I can't remember, but I think one of the those black wires going down to the trans switch should be hot all the time (or at least when the key is "on") and the other one should lead to a ground ??? Makes sense, but I'd have to look at a wiring diagram. It sounds like your light is getting 12V or ground from somewhere it shouldn't (whatever normally comes from the switch, assuming the switch is OK).

Lastly......I'm not sure about this....but I think the trans switch is just an internal push-button.....Is it possible to screw it in too far so that the button is always pushed????

The circuit is simple, the dash reverse light is triggered off 1 side of the 12V+ going through the single pole single throw reverse light switch in the 4 speed transmission. Track back the dash reverse light single 12V+ lead, sound like it is connected to the 12V+ input to the reverse light transmission switch. But should be on the output side of the switch so it is only hot when the reverse light switch is ON, ignition ON, transmission in reverse...

Note that the reverse light dash indicator has only a single lead as the 12V- is when the indicator is mounted and grounded. The transmission reverse light switch (2 terminals) both sides are above ground switching the 12V+, it has no ground connection through the switch.

Just my $0.02...

I had the same problem while I was under the dash I moved the shifter and then hit the steering col with some thing and then I heard a click ..well the switch at the bottom of the col was old so I sprayed wd40 on it not a problem since