The old bimetal flasher relay needs full voltage and current draw (amperage) to work. Without everything in the circuit working optimally, it will never flash, period.
HL power is only there while the engine is running, unless you rig a power supply using test leads/jumpers.
Sounds like you're missing a ground at the HL end of the harness. Based on what you've said, I'd pull the harness, test the continuity of every lead and completely unwrap it, if there's visible damage to the factory sheathing.
FYI, lead breaks between the frame grommet and HL shell are very common and can be tough to diagnose as the leads can appear to be intact and even test okay...intermittently. Wire harness diagnosis & repairs are much less daunting with the harness on a bench, rather than in-situ.