American dialectologists have evidence showing wait on (sense 3) to be more a Southern than a Northern form in speech. Handbook writers universally denigrate wait on and prescribe wait for in writing. Our evidence from printed sources does not show a regional preference; it does show that the handbooks' advice is not based on current usage <settlement of the big problems still waited on Russia — Time><I couldn't make out … whether Harper was waiting on me for approval — E. B. White><the staggering bill that waited on them at the white commissary downtown — Maya Angelou>. One reason for the continuing use of wait on may lie in its being able to suggest protracted or irritating waits better than wait for<for two days I've been waiting on weather — Charles A. Lindbergh><the boredom of black Africans sitting there, waiting on the whims of a colonial bureaucracy — Vincent Canby><doesn't care to sit around waiting on a House that's virtually paralyzed — Glenn A. Briere>. Wait on is less common than wait for, but if it seems natural, there is no reason to avoid it.
Examples of WAIT
I hate waiting in long lines.
They waited at the train station together.
You should have waited a little longer. He showed up right after you left.
I don't have time to wait around. If he's not here in five minutes, I'm leaving.
She waited behind after class to talk to the professor.
I'm sorry to have kept you waiting. How may I help you?
I waited and waited but he never showed up.
Wait! Don't start the engine yet.
We waited for the sun to set before starting the fire.
I know she was happy when I lost my job. She was waiting to see me fail.
Origin of WAIT
Middle English, from Anglo-French waiter, guaiter to watch over, await, of Germanic origin; akin to Old High German wahta watch, Old English wæccan to watch — more at wake