I would be surprised if the third brake light mounting isn't the problem. The light housing slides rearward into a pair of guides that locate it on two electrical contacts. Remove the light rear cover, in this case it will be the front as you look back at it from the seat. With the cover removed a attachment clip should be located and releasing it should allow the lamp housing to be removed. The contacts should then be visible, prior to testing with your meter use it to test battery voltage, I have seen many failed voltage tests due to equipment. With that being said you will test acrossed the two contacts for system voltage with brakes applied.
Bill