No. That is, not necessarily. I did not read that the OP had checked for switched brake light power going INTO the turn signal switch. Could be a problem in the brake like switch circuit, or the switch. IT COULD ALSO be a problem in the TS switch itself.
You cannot make assumptions. You have to get DIRTY. You have to ROLL UP YOUR SLEEVES, and you have to get out the wiring diagram, a meter, clip leads, test light, maybe some spare bulbs and GO TO WORK
Start by finding the brake light switch wire, normally white, that enters the turn signal switch connector. That circuit is operational at all times, no key needed. Probe the connector and depress the brake. Should have power with brake pedal depressed. If not crawl under and access the switch. One side of the switch should always be hot. If not find out why. If the output of the switch is not working, either the braket/ switch is loose/ out of adjustment or a bad switch
If you DO have power out of the brake light witch (entering the column TS switch, now look up the wiring code for the rear signal lamps and probe them. With the switch centered, you should have brake power there when the pedal is depressed.
If you DO have power there, it's a LED / grounding issue. If you do not, then you have a TS switch issue.
