Brake light doesn't flash it's 2nd diode when braking

You are right that there are two switches: on right under brake leaver (a small plastic thingy), and second is connected to your brake pedal via a small hock on the back of brake pedal actuation mechanism. It should be easy to troubleshoot if one or both don't work as intended, as both switches should have a connector to disconnect from main circuit. Images from ebay attached (sorry, don't have access to my bike now). Read on below the images if switches are in good order.

This is rear brake switch (right foot pedal):


This is front brake switch, or something very similar to it (front brake hand lever):



There are two contacts on the back of the bulb and corresponding number inside bulb socket of a brake light. Jacket of the bulb socket is used for negative (common) and one of the contacts inside socket is used for running light positive, another is used for brake light. If you have a voltmeter/multi-miter, I would recommend checking that you get voltage only on one recessed contact when brake is not engaged. This gives you running lights.
If you get voltage on both, it probably means a problem with brake switch at the foot pedal or hand lever (or even both) [see above if you skipped that part] or you have a short in the socket or in the wiring going to the back of the bike.

I'm not 100% sure, but I believe Suzuki C50/90 from that period feed both voltages (running and brake) simultaneously to the bulb (in series) when braking. So regular halogen bulb would have both filaments light up. LED bulbs are usually smarter, and they light up when either or both contact get voltage, just change light intensity.