The (relatively ) short answer to your question is that you can add some load resistors and it'll almost certainly fix the problem you're describing. You don't need to do all four corners; I'm using load resistors on my rear turn signals only (they're easy to affix the the rear of the housing) and don't have any problems. IIRC (unfortunately, I don't believe I kept good records when I did this years ago), I actually added them to solve another problem (I think I was dealing with some weird interactions between different types of front and rear turn signals at the time; I think those problems were due to older LEDs that didn't have reverse voltage protection diodes in them). Anyway, I have no such problems with my turn signal indicator, and it's probably due to the presence of the load resistors and/or the fact that I'm running LEDs in my instrument cluster (which requires very little current to illuminate).

The long answer is to understand why this happens. Have you ever noticed that the turn signal indicator blinks out of phase with the turn signals themselves? (i.e., if you've turned on a turn signal or hazard lights, the indicator is on when the turn signal(s) are off and vice versa)

That's because 3-terminal flasher relays are wired something like this (the 928 is more complicated, but the operation of the turn signal indicator with respect to the relay is pretty much the same).



The main thing to notice (if you can read schematics) is that when the turn signal lever is switched on (either direction), the indicator light will be off when the relay closes (and the turn signal lights turn on), but it should turn on when the relay opens because the indicator light still has 12 V connected to one side, but the other side is then grounded through the turn signal lights, which (in their original incandescent form) are much lower resistance than the indicator bulb. So... raise the resistance (and the LEDs are effectively much higher resistance than the original incandescents), and... indicator bulb no longer has a good low-resistance path to ground. QED

There are probably other ways to solve this problem (e.g., reworking the way the indicator light works), but it probably is most expedient to just solve it with load resistors.

I'd suggest experimenting with the highest value resistors you can that get the job done. I can't tell you what values I used (I'm at work and my car is at home), but 25 Ω load resistors and 6 Ω load resistors are quite common. Remember: the lower the resistance, the more current the circuit will draw and waste in the form of dissipated heat.