My indicators did exactly the same thing for a while (slow on idle, fast when moving) and then they packed up (on a roundabout on a right turn - handy!). The flasher unit was at fault either no flash, lights permanately on or a light show more like a disco.
I tried contact cleaner, bit of emery cloth, it helped but the unit was too temperamental. I drove over to Halfords with the rating (12v 2 x 21W + 5W) and found a two contact flasher unit more by luck than chance.
Bingo... all sorted.
I think it was meant to be for some Hyundai. I now have very Japanese sounding indicators.