Check the connections before replacing the switch. Grounds are gremlins on TDrs.
Also make sure the car is actually shifted into reverse. When I was putting together my Spyder the backup light gave me a heart attack when it wouldn’t work despite my shifting it into reverse to test. I checked the light, the wires, connections and even the switch itself; no joy. I thought reverse gear might be fouled up inside the transaxle….
Then I rolled the car in gear and watched the flywheel. Turns out what I’d thought was solid reverse was just second gear again, because my home-made shifter linkage bracket (it’s a cable shifter; everything is backwards on the Spyder compared to a Bug or TDr) was allowing a tiny bit of deflection.
Welded up some new junk to the bracket and Bob was my uncle.
Obviously your car’s linkage is simpler. But do check to make sure reverse is engaged before proceeding with the other stuff.