I know nothing of the car's history...I just purchased it, but I'd bet that this isn't due to a modification. I talked to the previous owner, and he said his mechanic said it was the "wiper module"(???....eh?).
I can tell you what it "isn't" from switching "known good" parts from another W124 I have here for sale and a little more research. It isn't the "mutifunction relay" or the headlight washer relay, or the wipe/wash switch. Also....I was mistaken on the headlight wipers....they don't arbitrarily park straight up....they park wherever they are when you release the washer switch (with the headlights on).