67 Dart 270 reverse lights always on...help please

whats the best way to check this switch's viability before spending cash on a new one?

First I would disconnect the connector and check if the backup lights have turned off. if so then there is an issue in the switch or mechanism.

If not then you have some other wiring issue to deal with, start tracing wires with the help of the service manual.

after the test above I hate to say this but you would be best to remove the switch from the column. That way you can activate it without being a limbo champ.
Once removed look for the actuator lever on the shaft. move the gear selector through the gears and see that it moves freely. ( don't forget parking brake and / or tire chock)
once out you can then bench test it. there is one position where there should be 0 ohms ( short cir) between the two pins on the connector coming from the switch. all other positions there should be infinite ohms (open cir)

When I troubleshooted mine it was not working at all ie no backup lights. The lever was there and moved freely the switch would move but no 0 ohms in any position. I drilled out the rivets and disassembled the the switch. I found that the springs that push the brass bar to the contacts were corroded away and the main sporing the returns the switch to the park position was in 2 pieces. I thought about finding new springs but ultimately decided to just buy an NOS instead (VERY PRICY so keep your eyes open on Ebay and FABO)

since yours are on all the time I suspect the bar i referred to before is stuck on the contacts OR you have some other wiring issue.

good luck.

PM me with your email address and I can send you some photos of the switch disassembed. I helped another member here in the last year with his switch ( console switch but enough similar parts that my column switch was able to do the trick for him.)