The buzzer is part of the wireless door lock system that is standard in all 03/04 4runners, wether or not you have one of the two available Toyota alarms.
Do your door lock system, interior lights, signal flashers, door lock indicator/security indicator (red flashing thing on dash) and alarm otherwise work normally?
There is no connection between the door lock system and the speakers. If this problem happened after a speaker upgrade, is it possible you jarred something else loose while you were inside the doors panels?
Perhaps this information from the service manuals might help.
Buzzer Sound Function
During lock operation, when the body ECU receives a lock signal from the door lock detection SW, the wireless door lock buzzzer goes on once. During unlock operation, when the body ECU receives an unlock signal from the door lock detection SW, the wireless door lock buzzer goes on twice.
With any door open, when the body ECU receives a lock signal from the transmitter, the wireless door lock buzzer goes on for apporx. 10 seconds. If the door is closed, or ignition SW is on, or if the unlock signal is received from the transmitter while the buzzer is on, the buzzer stops.
Visual Confirmation of Lock or Unlock
During lock operation, when the body ECU receives a lock signal from the door lock detection SW, the turn signal light is flashed once. During unlock ..., the turn signal light is flashed twice.
Repeat Function
If the lock detectionsignal in response to the output signal is not received after the body ECU has output the lock signal, the lock signal is output again.