From my own personal experience, when i heard a clicking sound i didnt know what it was. After a week i noticed my shifter moved back and forth alot. and had some grinding noise, almost like the gears were not meshing. The symptoms i was experiencing was a snap ring failure. after getting it fixed i came to the conclusion that the ticking was the broken snap ring.
I dont know what year your NSX is but if its '91 or '92 and the ticking sound sounds like you got a rock stuck in between your tire tread, then it could very well be the snap ring.
Good luck.