09 Prostar humming under fuse panel in accessory mode

Put your finger on each relay when this happens and see if it is a particular one.

 

Could be the low voltage disconnect but I don't think you can stop it

 

The low voltage kick out cannot be mistaken. This called load shedding and is body controller controlled. When it senses about 12.1 volts the dash will beep annoyingly and the dash display will read "LOAD SHEDDING". The relay for that is under the center console right infront of the shifter. Under the fuse panel is the heater box. Closer to the floor is the linear power module for the blower motor and ABS module. Nothing else but wires. This is an area where some installers put in equipment for satellites or other devices. Does your truck have anything like this?

 

If this happens exclusively only when the radio is also on, I would have to assume the radio is involved some how. I wonder if it is wired correctly and has a good ground. In that same area under the fuse panel is a couple of actuator motors for your heater box temp blend/mode and recirculate. They may be the source of the noise. If you open the passenger door and stand outside on the passenger side, can you pinpoint closer to where you hear it? Is there any chance it is from the door speaker?

 

Without seeing it, I really don't know what to tell you. You'll just have to experiment by turning things on/off one at a time to see if it effects it at all. You could also try pulling your breakers one at a time to see if a particular circuit or accessory is at fault.