Assuming all your connections are OK, it sounds like your wiper motor is in need or repair or replacement, since if it's drawing excessive current, the motor rotor might be frozen. If I recall correctly, it's the passenger side motor that not only controls the wiper, but also switches on and off the pump motor at certain intervals too. Apparently, corrosion is a common problem in the motor units, esp. after a lot of years.

If you have the time and inclination, there is a detailed explanation by Jon Kanas in Colorado of the MBCA for disassemby and repair of the W124 headlamp wiper motor at:

http://www.qadas.com/~kanas/300TE_Headlight_Wipers.html

Personally, I had one that I spent numerous hours on (it had erratic operation), and I never did get it fixed properly. Ended up buying a new one instead. But, your's might be worth a try.

good luck...dan