I have had some experience with this area, even making my own DB10 Relay substitute, described in Lotus Europa Central.
The brake, hazard and indicator functions share common wiring from the relay to the bulb, so if the indicators are working there's little point in trying to trace a problem there.
Try this - test the brake lights with the Hazard Switch in both the On and Off positions. I think that if the switch is On, but you have a faulty hazard flasher unit, you will get the symptoms you describe. Worth a shot, anyway.