For what you want, just build another C2 RGB Encoder for your Cadet system and don’t patch anything to the inputs. This will give you black video output and serve as a black burst generator.
The other option would be to make a DIY circuit that attenuates and buffers the CSYNC on your sync bus and drives it thru a video op amp buffer. @reverselandfill has incorporated this approach into his sync busboard design, with the full thread located here:
Alternately, you can drive the Vidiot from Visual Cortex’s sync out chain on the rear of the module.
The CSYNC on the 14-pin sync bus is TTL level (5V logic). When you attenuate it to 0.6V, buffer with video opamp, and drive thru 75R resistor, it is now “black video.” (Not quite black burst, which also includes subcarrier embedded along with CSYNC, but that’s a different topic.)