Possible overcharging?

My '01 XG300 shows the parking brake and battery warnings when I start up. If I turn on the rear defroster, headlights or air conditioner they go out. Battery has been checked, apparently OK.
After the car has been running for a while, the lights go out by themselves until I increase the revs, when they both come back on; turning off again when I idle. Could this be some kind of overcharge problem?

Well, I found the promlem was due to some wierd alternator defect. The dealer replaced it and all is well... except that the installed cost was $865!