I have a 1991 RX-7 convt. and when I put on the high beams the high beams stay on for about 2 seconds then switch back to the low beams .Never had this problem in the past and local Mazda dealer does not have a fix.

 

Find the dimmer relay located at the very front of the car (next to the headlight relay) as it has 5 wires with one wire being solid White. W/the low beams on, ground the White wire at the dimmer relay and see if the high beams stay on. If they stay on when the White wire is grounded then the dimmer switch in the dash is probably the cause of your problem. When you pull back on the lever of the dimmer switch it is supposed to send a ground signal to the White wire of the relay so as to tell the relay the high beams need to come on.