weird sound through speakers when radio is turned on. on 1991 BMW 325i

Hi, this only happens when the radio is on (ofcourse). Any action which utilizes current, such as stepping on the break which means the break light turns on, using a turn signal,turning on wipers gives me an audible "poof" like sound to eminate from the rear speakers. Clearly it must be the sound system (it is the original one) but I don't know where to start. Has anyone experienced this before and do you have any suggestions on where to start. I don't want to install a new radio since, once it's on, there is no problem with the sound...
Thanks in advance!

Asked by for the 1991 BMW 325i
Check for RF interference. Any new bulbs been replaced recently? It's not the radio but the wiring having poor insulation somewhere. Check the basics...
Thanks for the response. No, no bulbs have been replaced and are all functioning fine. I am sorry I didn't indicate that I am a novice at anything automotive, however, I am an experienced computer hardware troubleshooter. Your answer makes absolute sense, but I am not sure where to start checking the wiring. In the back from inside the trunk or under the dash? Thanks for your help!!
It's probably back under the accessory tray where you hear the noises from those speakers
I'd love to know what exactly can cause such clicks and how to fix that? In my case I tried to disconnect speakers wiring and still can hear these clicks.
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