I don't have an answer but I have some information to share. I have had the same issue on both my 74 and my 80, namely the ts indicator would flash once and then no more while the actual turn signals continued to operate. First off, I think everyone understands that the stock wiring circuitry is not robust and has inherent issues, hence the brown wire mod and relay mods.
On my 80, I have been going through the all the electricals to correct non-functionalities and make improvements. I cleaned all of the fuse panel connections and did a headlight relay mod. Still had the ts issue, but good headlights. I pulled the Instrument panel cleaned all the contacts, replaced the small 74 size bulbs where needed and put in LEDs on the instrument panel lights. After this mod, the instrument panel turn signal flasher worked properly. I assume I somehow improved the voltage supplied to the ts light, but can't pinpoint one specific thing. Never messed with the flasher unit.
On my 74, I went through the fuse panel, cleaning everything and mending the failed female spade connectors. Some of them had one side fail leaving a loose connection. After this maintenance, the 74 ts indicator worked sort of properly. It would blink while turn signal blinked, but its speed varied with the car electrical load. In particular, when driving at night I put on my ts, the indicator would blink appropriately and then when I stepped on the brakes it would blink noticeably slower. I read a post by Bob Brown saying that the brake lights had a huge current draw, so I recently replaced the brake light lamps with LEDs. Now the ts indicator light does not slow up when I put on the brakes. Again, never messed with the flasher.
I'm a decent car electrical tech but not an EE to compute voltage drops across the circuits. Overall, I think there are two things going on. First the hardware is old and needs to be cleaned and repaired. Second, the non-robust design needs some help getting the necessary voltages and currents to the components. So I'm doing the relay mods and installing LEDs bit by bit and seeing incremental improvements as I go.
That's all I got. Not an oaken stake in the heart, but maybe a wreath of garlic. Good luck and best regards, jrt.