Since the issue is with the parking light circuit, and the magic smoke came out of the dimmer area 'o life...
... I'd start there ...
The tailights and instrument panel lights share the same fuse.
It's quite likely your problem is in the gauge/illumination area of the circuit, given the fact that the dimmer went up in smoke.
Got any boost, egt, or other gauge illumination circuits tapped into the instrument panel lighting circuit?
Made any changes to the wiring there recently?
Unplug the dimmer rheostat, and put a ten amp fuse back in the circuit, and do a light check.
If the fuse survives this test, the issue is in the instrument panel illumination circuit. I would start checking anything aftrmarket first, and then just start checking the harness and bulbs that are controlled by the dimmer. You'll probably see a wire that's all crinkly/wrinkly, that's the one that's been carrying all the current. Follow it to the end and you've probably found the problem.
If the fuse pops immediately when you power up the light, you'll have to check deeper into the rest of the tailight circuit.
edit never subsitute a higher fuse rating to troubleshoot a circuit!
You're lucky if all you fried was the dimmer.
I've seen whole wiring harnesses get smoked playing fast and loose with the fuse ratings. /ubbthreads/images/graemlins/bawling.gif
don't do it