Could be Pilot bearing
Maybe throw out bearing but fits Pilot bearing more from your description
The pressure plate is bolted to the fly wheel so spins at engine RPMs all the time
The input shaft from transmission spins at transmission RPMs, so rear wheel RPMs when in gear.
Input shaft is supported at the end by the Pilot bearing in the center of flywheel/crank shaft
This allows the input shaft to spin at a different RPM than the engine.
When you push in the clutch pedal the Throw out bearing pushes in on the pressure plate springs which releases the grip on the clutch disc
This could cause a clicking noise if throw out bearing was failing but noise would happen even if transmission was in Neutral, just pushing in on the pedal would start the clicking.
OK, so clutch pedal is in and trans is in Neutral, no clicking
Input shaft is still spinning at engine RPMs
To put trans in gear you have to slow the input shaft down to rear wheel RPMs, so if stopped input shaft has to go down to 0 RPMs
Now this is when Pilot bearing's use comes in, it allows input shaft and engine RPMs to be different, so as you put trans into a gear input shaft is slowed down, and if this is when you start to hear the clicking then it would most likely be Pilot bearing failing