If it's the PTO clicking, and not just the switch, then that's very confusing. The click of the PTO itself is it getting about 13.5v and then magnetized, pulling the two components together. When that happens, when the engine is running, there's almost no way for the PTO pulley's to not turn.
Especially since it was only a few seconds from the time you disengaged it to when you reengaged it.
When I need to see something under the mower, when running, I'll prop my phone up somewhere on the ground level, and record video.
I suggest you try this method. I'm not sure what phone you have, but most of them today can record video. Aim the phone, click record, get on the running mower, engage the PTO, then simply watch the video.