So it was a burned out fuse, I .replaced the switch to no avail. Replaced it with another 15 amp fuse. Last night it blew again. Replaced it with a 20 amp. Will using a 20 cause any serious harm??

fuses are rated for the circuit they are intended to protect.
using a higher rated fuse than the circuit is designed for is not a good idea.
you will have to look further into the tail light branch to see what is causing the fuse to blow.

Id look for the possible cause. Heck, my 05 peon has never tossed a fuse and still has the org. tail light bulbs, plugs, wires, hoses, ect.. ha ha. Great cars.

Every couple years, the R/R tail lamp on my '96 Breeze quits. Condensation gets into the housing and corrodes the bulb carrier.
I either clean it or replace it, and that makes it happy.
Never blows a fuse, though.
But maybe worth a look if Neons use the same kind of design.

and will add the following:

It is possible you have a bad batch of fuses, our overseas QC is not always 100%. A 15 amp fuse would normally be used in a circuit that draws ~ 11A max.

Do a current draw on the circuit to see what it's actually pulling. Also there are usually other items that may piggyback on the same circuit so a schematic may be handy to identify what else may be on that circuit causing the problem. keep us posted