I enjoy those LED's across the top to indicate audio output. That's a nice looking box of the later generation
Being mechanical minded I will offer my opinion. It seems to me that since the clicking on the left deck starts when powering up the right deck that both decks are powered by the same motor and/or their drive motors are powered up together. My situation was caused by the motorized mechanism cam gear but this unit (by appearance) seems to be fully mechanical (your finger pressure engages the heads) even with the stereo unplugged and powered off.
If all of this is true, pressing pause stops the noise and in play mode it stops it as well I am going to go out on a limb and say that it may have something to do with the auto-stop part of the mechanism on the left deck. That deck is going to have to be inspected for loose and or broken/missing plastic pieces. It sounds to me like it believes it is still in play mode and is trying to kick the head back up for an auto stop as long as its flywheel is spinning and not engaged.
There are many things it can be but one thing is a 100% certain...it's a mechanical issue with the left deck. A sticky part, a missing broken spring, a cracked/broken gear. No way to tell without digging in
