I have a 1989 190E 2.6 Automatic

About a month ago I turned my car off after some highway driving, a
couple minutes later I tried to start it again and, at first... I had
to keep turning the key on and then off,  nothing, then some ticking,
then it slowly it started to turn over... and eventually started. The
strange thing is that the wiper came on for one pass when the car
started.

For the last couple of weeks, it has been a hit and miss thing.
Sometimes I turn the key and get nothing, other times "tick",
eventually there is always a slow turning over that eventually starts
the car. The wiper does one pass for 99% of successful start ups that
take more than one try, I have also notice a mild sulfur (rotten egg)
type smell.

Yesterday I couldn't get anything more out of it than a feeble and
unsuccessful attempt at turning over... again the light sulfur smell.

The battery strength seems fine, the alternator seems to be fine.

Any ideas? I would say starter of solenoid, but this wiper thing is
leading me to guess that there is a short. Can anyone help? I
appreciate whatever advice you can give.