Yes, the more I think about it, the more I see the issue with either the relay or the combination switch. When you hit the washer it pulses the relay and makes it cycle.

My combo switch had really gummy contacts in the wiper section. There may be a parasitic short that carries just a bit of current over to the relay on startup. Just a pulse of high frequency noise as you close the key switch. Just enough to start the wiper cycle.

Moving the mirror puts big inductive loads on the 12v circuit and this may also be enough to bounce the relay through a dirty combo switch. Disconnecting and connecting a dc motor can cause big spikes.

So why does changing a relay help? My guess is that there is some filtering circuitry in there to prevent spiking/glitching from triggering the relay. Any sensible engineer would put something in to discriminate between false triggers and real signals. Perhaps a capacitor resistor circuit that degrades over time as the cap dries out.

The guck in my switch looked like a combination of grease and ground copper. A perfect medium to transmit arcing noise.

Just a theory. I guess my advice is clean the contacts then change the relay if things persist. Cheap fix first.

Edit - spoke too soon. My car still has this problem. On to the relay.

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79 300TD “Old Smokey” AKA “The Mistake” (SOLD)
82 240D stick shift 335k miles (SOLD)
82 300SD 300k miles
85 300D Turbodiesel 170k miles
97 C280 147k miles