There's a specific LED thread for the dash lights.

http://www.peachparts.com/shopforum/showthread.php?t=243687&highlight=year

"Cooking" the rheostat may be less likely than burning a circuit trace on the panel. You can bypass the rheostat pretty easily.

The console lights are on the same circuit and downstream of the dash, so yes, they're related. Maybe the shifter light specifically is not, but the CCU lights and the radio illumination are.

Understanding the prism design and the light "channel" and getting everything cleaned of 25+ years of haze can improve the lights without going to the LEDs.

If you really want/need 'great' illumination there is a Canadian company that eliminates the prisms and installs "direct illumination" LEDs, put it's pricey.