Your issue is electrical. Water gets to an electrical component of the wiper system and shorts it out or causes it to stop working. Water would not effect the gear system to a point where it would not work wet but would work dry. If anything it would imped operation when dry as the water would dislodge/remove the grease. Unless some parts of the transmission assembly are broken and somehow dry helps movement...gotta be electrical.
The only electrical component of the wiper system is the motor itself. This is from a w201. Its most likely very similar to the one thats on a w124/etc
Here you can see the wiper, wiper transmission and motor. The motor sits near the edge of the windshield, which makes it possible that water is falling on it and somehow getting to its internals.
I recommend taking the cowling off and observing the system dry, and wet.
__________________
Cruise Control not working? Send me PM or email (jamesdean59@gmail.com). I might be able to help out.
Check here for compatibility, diagnostics, and availability!
(4/11/2020: Hi Everyone! I am still taking orders and replying to emails/PMs/etc, I appreciate your patience in these crazy times. Stay safe and healthy!)
82 300SD 145k
89 420SEL 210k
89 560SEL 118k
90 300SE 262k
RIP 5/25/2010
90 560SEL 154k
91 300D 2.5 Turbo. 241k
93 190E 3.0 235k
93 300E 195k