So the issue only occurs when indicating right, AND you're missing a bulb in it.
Normally on old flasher relays, when a bulb blows, they start to flash quicker. If you have potentially another short, or a couple of lower resistance bulbs, the constant noise you might be hearing is actually the flasher relay dropping in and out really quickly.
I suspect if you get your front indicator wired in, your symptoms will change...
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