I would add that you really ought to first disconnect the positive lead to the battery as the switch has hot leads to it and your
dash area is well grounded so a short is easy to cause.
it is most likely that the rheostat coil in your switch has
burned out, causing your dash lights to fail. If you don't want to buy a new switch, you can fairly easily solder a jumper wire around the rheostat. Your dash lights will work fine, although you will no longer be able to vary their intensity (a feature I have always considered fairly worthless).