Overly high resistance can cause indicators to stay on and not flash (the opposite of fast flashing because of low resistance LEDs being fitted without ballasts). Commonly it is caused by folk fitting bulbs of a higher wattage than recommended, but this is clearly not your problem. Fitting ballast resistors of too high a resistance with LED indicators could also feasibly cause this issue, but as you say it only does it in the wet, it can't be this either.

So I would hazard a guess that you have a poor connection somewhere, either positive or earth (more likely an earth) and, as both sides are affected, I would point an accusing finger at the relay's block connector, or possibly the handlebar switch itself. Any poor connection will, as you'd expect, be made worse by rain/damp.

Check all of the above and see what you turn up...

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