[morzh]

Eric

It is hard to get the point as if you touch a trimmer cap (without pressing) with an insulated took nothing should be happening at all.

Now here's a guess: when you touching it you do fix some cold soldering spot which developed long time ago and you triggered it when first touched the cap.

Take a soldering iron.
Turn the radio fully off / unplug it from the AC.

And touch up with a goodly portion of a rosin flux EVERY contact around that can be possibly flexed when you touch the C404.
All of them - coils and caps.

Then tell us the result.