I've had this same issue (two wiper sweeps every time I started the engine) in my 1984 YM W123's and fixed it by replacing the wiper relay, it's way back behind the speedo binnacle, you jhave to remove that to access the relay .

Pelican Parts has a nifty little DIY 'How To' with good photos of what to do .

__________________
-Nate
1982 240D 408,XXX miles
Ignorance is the mother of suspicion and fear is the father

I did then what I knew how to do ~ now that I know better I do better