Backlighting/Dimmer Switch Fun -- Cherokee 140

I have been experiencing an odd problem with my digital EGT/CHT gauge.
The backlighting on the guage is controlled by the panel light dimmer
potentiometer (or rheostat, which ever it is). When the dimmer switch
is off, the gauge works fine. Once I turn the dimmer past the click,
the instrument backlighting comes on but the digital readout goes
blank. As I turn it further, the digital readout may or may not show
up, and if it does, the reading is inaccurate. Once the dimmer rotates
to full-dim, the display behaves normally again. I took a quick look
behind the panel, and didn't see anything obvious. Of course, there are
about a million wires crammed back there and I was laying upside down
on my head at the time. Any ideas?