Ok. Here is my guess.
Turn signal flashers are controlled by heat that is created by a resister inside the flasher can. This heating resister is located near a bi-metal strip. This strip opens and closes the circuit to the TS lamps. This resister is wired in series with the turn signal lamps and with the bi-metal strip/switch.
When the turn signal switch is open the resister is not in the circuit and remains cold and bi-metal switch is closed.
When the turn signal switch is closed current flows through the TS lamps and the resister that begins to heat the bi-metal switch. When the bi-metal switch is heated enough to distort and break the circuit to the lamps, current stops and the heater cools and the bi-metal cools permitting the bi-metal to return to it's closed position thus lighting the TS lamps again.
The bi-metal switch is made from (2) dissimilar metals that will expand at differing rates when heated. When these metals are welded together (thus the term bi-metal) and heated they will distort unevenly.
The noise is coming from the bi-metal strip/switch that due manufacturing tolerances such as incorrect tension in the switch or poor welding of the (2) metals is reacting to a sudden inrush of current created by the TS lamp filaments low cold resistance and initial cold resistance of flasher heater.