Here, during our old test, we had two problems.
First, while sitting in the room, we could perfectly hear what the operator was doing with the connections. We just had the headphones plugged into one amp or the other. But the noise was different. Plugging inside amp1 made "clunk", while plugging inside amp2 made "klang".
Second, while wearing headphones, we could hear the connection inside amp1 thanks to a faint static noise "click" in the driver, while plugging the headphones inside amp2 made no noise.
The solution that we found was this :
The listener was constantly sitting, turning his back to the setup. He could ask to listen to what he wanted (play, pause, play, restart playback, please etc).
Both amps output ports were plugged. One with the headphones, the other with a dummy plug.
Headphones cable was running below a heavy book, so the that listener who is wearing the headphones can't feel the cable moving left or right.
The listener could ask to listen to A, to B or to X at will. For this purpose, the listener would
-Tell "Amplifier A, please"
-Put down the headphones on his lap (to avoid hearing the click)
-Cover his ears with his hands and count aloud "ONE TWO THREE FOUR FIVE" ! We found that this was enough to prevent him to hear the noise of the cables and plugs making "klunk" or "klang". During this time, the operator had to unplug headphones and the dummy plug from Amp1 and Amp2, then plug them back in the required configuration (here, headphone in Amp A, dummy plug in Amp B). The dummy plug is just an extra precaution, as the listener can't hear what's happening anyway while covering his ears and speaking aloud.
-Put back headphones onto his head.
EDIT : I forgot, the operator has to keep the headphone's jack and the dummy jack in hand while switching, because (if we don't cover our ears) we can clearly hear the noise of them being put of the table, and thus recognize which one is being manipulated by ear alone.