Yes, if you change the sentence like John suggested it would be grammatically correct.
Please wait for me at the school gate.
We use 'wait for' to tell someone who or wait we are waiting. We also use 'wait on.'
Wait for has the general meaning of anticipating/expecting something to happen, for example: 1. wait for a bus 2. wait for the rain to stop before going out 3. wait for a letter to arrive.
Wait on is in a way serve/act as servant. In a restaurant a waiter obviously waits on the customers. Wait on is also used, mostly in American English.
I would say most native speakers don't think about the grammar here, they just say what comes naturally to their minds. Using for in your example would be most grammatically correct.
at the school gate: we always use at when we are telling a general location we will be to meet someone. 1- I will meet you at the bus stop. 2- She is going to the meeting now. We will meet her for lunch at the restaurant when she finishes. 3- Are you friends meeting you at the park?
Hope this helps! Good luck!