If you are not getting key on power to the flasher, THAT is the area you need to check. Should be simple Power should be going through key, fuse, to flasher
The functional path is key---(in ACC? or "run")--to whatever fuse supplies flasher--to flasher---out of flasher---to TS switch.
Hazard flasher has power at all times
Inputs and outputs to TS switch:
IN:
TS flasher power with key on
Hazard flasher power at all times
Switched brake lamps power at all times
OUT:
Left and right rear turn/ stop
Left and right front turn, branched off to indicators