Brake lights stopped working

May be a bad switch. "New" does not mean "good."

Access the left kick panel and get into the connector which feeds back to the tail. Get your wiring diagram and identify the wiring. That way you can probe that while you are manipulating the switch.

With the switch centered, first double check that you are getting switched brake light power from the brake light switch TO the TS switch, check this right at the TS switch connector

Then move your meter to the left and right TS / stop light wires in the left kick panel. You can confirm right after taking a reading by actuating the TS switch/ key on and confirm you have the TS working.