Later BJ8s (he says he has a '67, but the "year" of a Healey is mostly meaningless) do not have that relay on the inner fender. The failure to come on when the brake pedal is pressed could be due to the bulbs, the light sockets (corrosion), the wiring (loose connections), but is most likely the brake pressure switch on the right inner fender. I got tired of replacing this switch, only to have the replacements fail in a short time. I replaced the pressure switch with a mechanical (adjustable) switch that operates off the brake pedal. It has the arm and roller described by mgtf328. That switch has operated just fine now since 2006.