in the drawing I attached that same 12v should also be on k10 pin 87 and is what feeds thru the relay to pin 30 when k10 energizes, to light the brake lights. it may be you have a bad connection somewhere along the source path from K6. it delivers measurable voltage unloaded and enough current to energize k10, but not enough to light the rear lights like the flasher does. IE: voltage is not good until it measures good under load.
You can wrap a small bare wire around K10-30 that sticks out from under the relay far enough to sample the voltage of the intact circuit when you step on the pedal with the normal load applied. What does that voltage look like?
You can also do the same bare wire test to measure voltage on the loaded circuit at K6-87 and D-1A... This might show where the circuit is breaking down and not flowing enough current to maintain full voltage under load.