I'm not familiar with the 8010, but this sounds like a dirty switch....
Indeed! I did some more thorough testing while reading the manual (how novel), and I now believe that the audio problem was the result of a combination of a dirty switch, and the fact that I didn't know how FM muting worked.
There's a bad connection in a couple of different switches, most notably the Tone pushbutton, which toggles the Bass/Mid/Treble knobs. It is scratchy when I push it in, and when I put pressure on it in a certain way I can reliably cause it to crackle and drop the right channel altogether, just the problem I was experiencing, except now it only fails during the moment when I'm pushing the switch. I think this is a result of blowing out the massive quantities of dust and then working the switch a few dozen times, which probably had the effect of wearing through the crud to form a better connection.
Never having had a decent analog receiver, I wasn't aware that some of them had an FM muting feature. When I first tested the receiver, it was at the place of purchase, in a large city with a lot of strong FM signals, even without an antenna attached. Under this condition, I experienced the scratchiness of the switch, but could at least tune in stations. However, when I got it home to a smaller town about an hour away, there are no stations strong enough to overcome the FM muting without an antenna. At this point I could receive no FM stations at all, and being unaware of the FM muting feature, was worried that this was a more severe symptom of the same problem. Understanding this problem was made slightly more difficult because the Stereo indicator bulb is burned out. I was clued into the true cause when I turned off muting (i.e. switched to FM mono). Further discovering that while in muting mode the darn thing worked when I touched the antenna contact (and also discovering that sometimes it pays to read the manual), I attached an antenna–actually just a wire until I can get a proper antenna–and it works fine with the exception of a little scratchiness only when working certain controls.
The station indicator needle is within 0.1 MHz of true (good enough); I don't fully understand FM alignment but from what I've read in the forums it sounds like a needle that is pointing in a significantly wrong place can be a sign that someone may have been monkeying with the alignment. (Though maybe I misunderstood that.)
Now that I know it's useful to me in its current state, my servicing priorities have changed.
1. Clean the switches
2. Replace all incandescent bulbs with LEDs (most of them are burned out anyway)
3. Get a bajillion capacitors ordered and get to work on it
Gotta get me a desoldering station before I get to #3 I think. I would like to have one for work on the old Commodore computers anyway; it would help keep the ICs in those things cool when desoldering.