Re: Left signal cancels CC
The dome light thing doesn't make sense to me.
That said, I had a very similar situation on my '90. I had accidentally wired the stereo's primary power into the stock wire which lights the Ford stock stereo. It runs at full voltage normally, but once you hit the lights a resistor reduces voltage so as to dim the stock stereo.
Whenever I would hit my lights the stereo would cut out momentarily as power switched over, but it still ran fine on the reduced voltage. It could be that your stereo is more picky, and won't operate on anything less than 12V (I dunno exactly what the resistor allows for voltage).
Still, the dome light thing still doesn't fit.
Bottom line you need to just give your stereo nice, clean, uninterrupted 12V. So yank it out and hook the red wire up to such a power source, switched thru ignition if you wish. Yellow should of course be hot at all times for memory.