Ahh - It just dawned on me, I bet what may be causing it is a 'backfeed' through the dash indicator circuit which is producing a small voltage on the opposite-hand signal circuit.
Especially if your dash has a single flasher bulb vs. both right & left.
A bit out of my element with the electrical theory, so I'm speculating here - but:
With normal incandescent bulbs (low resistance, high amperage draw) maybe it wouldn't be enough to make the filaments glow, but LED's draw so little current that it could be enough to light them up?
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