This is a dangerous situation. Keep battery disconnected. Take switch out on bench, Test it's operation by continuity testing. Then be very sure you wired it correctly. Check each wire under dash for continuity to ground (a short as Steve said).
If all that is good you could hook up a 6V bulb to the rheostat/resistor/dash dimmer and to the park circuit using a 6V battery charger as a power supply (with inline fuse) to see if you can repeat the glow/smoke, outside the truck, on the bench, with this bulb as the "load". If you can not repeat the failure, then concentrate on wiring. Something somewhere is mis-wired or touching hot or ground when it should not. You can test the switch while hanging down on the wires, no need to install in dash where you can't see. You can also install the old switch to see if it does the same. While old or new switch is hanging down and wired up where you can observe/test, it may need a temp ground wire from it's metal bracket to chassis ground. It is possible the switch is bad but not likely.
Where exactly is it glowing? What is glowing? the windings on the rheostat? Sometimes when a switch gets mounted under the dash, the way you have the connections or wire routed lets a contact or unprotected terminal touch a place on the dash or a bracket under there. Think about anything else you have tinkered with before this test drive. Sounds like if everything is new, you rewired. Is this the first test after rewire/new switch? Hopefully the new wiring harness contained a new modern fuse panel.
