From what I remember, both plugs are genuine Suzuki items so what's adrift there I don't know.
Anyway, there's no need to use the genuine items, plenty of one way plugs / sockets on
ebay.
It should be possible to work out what goes where....the heater will have one wire and an earth (normally a two pin plug) and the others go to the mirror motor which relies on reverse polarity to get it to turn in different directions. For sure a wiring diagram would help as I can't comment on the wiring colours but an auto electrician shouldn't have too many issues.
Would the supplier take the mirror back?
John
