That's one of those "weakest link" questions. It is normal for the system voltage to drop at idle, because the generator cannot produce any output at such low rpm. So the engine, headlights, etc. are running on the battery instead of the generator. The voltage at the battery drops fairly quickly from around 14 volts down to 12.6 or so (and then slowly goes down even further).
It's also normal for the flasher to be sensitive to the amount of current through it. This is supposed to be a safety feature, so you can tell from the light on the dash when one of the turn signal bulbs is burned out. But it seems like, as the thermal flashers get old, they need more current to continue operating. Also, as the turn signal bulbs age, they draw less current (and produce less light).
So, could be the flasher, could be the battery, could be the wiring, could be the bulbs, or even the turn switch. Jonmac had this problem only on one side, which he eventually traced to corrosion inside the wire insulation! About the only thing not suspect is the generator (as it isn't supposed to work at idle anyway).
I got tired of chasing the problem on my TR3A, and just switched to a "heavy duty" flasher, which is not as sensitive to load current. I couldn't find a thermal flasher at FLAPS that would work properly, so I bought an "electronic" Tridon EL-13. It works great, but of course does not look original. One caution, though, the EL-13 plastic case is not very strong. If you use a clip to mount it, make sure the clip is not too tight. The case on my first one eventually broke from the pressure. But the second one is still working great (now on the TR3).