I have a 1999 RX 300 and AC blower runs intermittently (ON -OFF). Always have cold air available just blower not working all the time. Tried different temp settings and leave settings on Auto still having the same problem.

 

There may be a faulty connection, bad motor control module, or the fan motor may be dying. Next time it does not turn on...reach down under the passenger area (pull over if driving) and bump the plastic housing with the side of your fist a couple times.