Should I run a jumper wire from it to the climate control lights?
This is exactly what I just did and it worked. The dimmer switch doesn't work, but that didn't before. The lights don't dim when you turn the switch down, but the lights are working on the radio like normal now.
'90 Acura Legend LS V6 2.7 5MT ^
'87 Acura Legend V6 2.5 5MT
'94 Saab 900 SE V6 2.5 4AT