i would definitely replace the headlights switch and keep the original old one on the side for now.
Replacing the switch is not going to solve the issue but it will make diagnostics easier.
when you do test the lights, look for the accessories lights to the left and right of the steering wheel.
The lighter port, wipers switch, make sure those are lighting up when the lights switched is turned on.
then look at the center section of the dash above the transmission hump.
since you have a idiot lights car then you may not have the center 3 gauges. so look at the radio lights and clock if you have it and the gear selector,, if these are lighting up in some way then you know the circuit for the lighting is working.
basic operation of the head lights switch. it has 3 positions. all the way in is off. pull it out half way Dash lights and running/parking lights will turn on, turn it left or right for dimming, and all the way to one side and it clicks and turns on the door and courtesy lights for full illumination.
pull the switch all the way out and the headlights come on.
now the dash lights on these cars are a problem, age causes the blue light filters in the gauge cluster to turn black and you get almost no lighting from a new halogen 194 light bulb. so its possible they are lighting up but you can't see it.
I would test inside the garage, turn off all the lights, have a flashlight with you and test in complete darkness to see if something does light up or not on the main gauges.
now good chance you will need to pull the main instrument cluster out of the car, you might need to replace the main circuit board and you may need to replace the lighting sockets and lights themselves. but first you want to see if the electrics are working because if you go through all this work and it still won't light up then you have to really start digging into the dash harness for the broken wire.
i would recommend once inside the main cluster changing to Green LEDS and removing the blue light filters from inside the gauges. this will require taking many things apart carefully to make the modifications.
you might want to set aside a possible budget of 100$ or more to make repairs or modifications.
as a start i would budget for a definite headlights switch replacement.
now i would try to source an original switch which will be more money then a reproduction switch but there used to be issues with the reproduction switches not working or fitting the harness connector correctly. a nos switch used to run about 40$ while a reproduction was 15-30$
step #1 do a complete darkness test with the current switch and take note if any other inside lights are working when the switch is pulled.
step #2 replace the switch and retest.
possible
Step #3 removing the main gauge cluster and budget for a:
*new circuit board
*possible dash voltage regulator
*possible nos socket replacements(do not use the reproduction ones they do not fit or work right, the original black plastic tends to fall apart from the bulb heat and they need to be replaced, depends when you do inspection)
LED upgrade and removal of blue filters inside the gauges, this modification of removing the filters may not be reversible the plastic is brittle so when you try and remove the filters carefully the white plastic pins snap off and thus you commit to colored LEDS from that point on.
at least with step 3 you rule out problems with the gauges themselves and upgrade the lighting dramatically.