Your last comment says it will continue to make the noise when the clutch is released - in neutral or in gear ???

I doubt the problem is inside the box. That leaves the pilot bushing/bearing in the back of the crank or the throwout bearing.

I doubt its the pilot bushing/bearing as this ONLY sees use when the clutch is depressed and the trans is in gear (the input shaft is not spinning and the crank is). Since the crank and input shaft are always turning at the same speed when the clutch is engaged there should be no noise from that.

So that leaves the throwout bearing and this is a common enough problem. I can't tell you how you'd pinpoint it precisely but I can't see it being anything else given your symptoms and explanation.

A replacement is about $50 but requires the removal of the trans. Pull the driveshaft, undo all shift linkage, remove the shifter, undo wiring, undo speedo cable, support the rear of the engine, remove trans crossmember, lower the engine/trans, pull out the trans - STRAIGHT OUT or you screw up the clutch. Now you can replace the throwout bearing and put it all back together.