Hi Ben,
Try cleaning up all the connections in the indicator wiring, take bullet connectors apart, check the earths, check the bulb holder, try new bulbs.
You have a higher resistance somewhere in the left hand side (compared to the right) which is why they are going slower on that side.
The reason they go slow when the headlights are on.
For the indicators to work correctly they must draw a certain amount of current and your headlights when on, are dropping the amount of current the indicator bulbs can draw, to a point below their usable limit when combined with a higher than normal resistance somewhere in the indicator wiring.
Hope that makes sense.
Steve
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