My Integra did the clicking too like drchronic mentioned how it occurred because the transmission mount. Mine looked good while the engine was in but when I pulled it out the spot where the insert would go was torn almost all the way off.
I didn't even recall this situation until it was mentioned. My car did the same thing almost since the first day I bought it. It's been since November since I drove my car so I forgot mine did the exact same thing yours is doing right now. I'll get a picture of my mount and show you how it looked.
My tranny is still in mint condition and I even took it apart and nothing was wrong with any of the bearings, syncros shift fork etc. same with the clutch, pressure plate flywheel. I never would have thought it was the mount but I have a new mount for when I put my engine back in since mine was almost to the point of fully blown.
I'll show you a pic on how easily hidden the problem was with my mount in a few minutes once I find my old one lol