I just had to put a R.H. fan motor in my '96 Accord,
I was fooled for a time, since the left fan came on and went off with the AC, so I figured that was the AC fan... (I had little cooling while sitting still) but when I turned the AC off one day to troubleshoot... I noticed that the L.H. fan came on when the engine heated up.... soooooo..... I unplugged the R.H. fan and applied battery voltage directly to the connector... it didn't spin. Replaced the R.H. fan and all has been well with my AC for over a month now.
ON EDIT: I believe that on my car BOTH fans run with the AC... could be wrong but I think I saw that, may have been a fluke... not sure right now, will check when car is cold tomorrow.