I wrote that wiki article, and it was the first thing I thought of when I saw the post title. That said, I don't think this is the OP's problem. I think the issue here is electrical, though I am not sure exactly how. The wild-ass guess by melt is actually pretty good, I'd check that out first.
Some vintage Vespas turn OFF the brake light by grounding to the body when the rear brake foot pedal isn't depressed -- not sure if the ET2 uses the same trick or not (probably not) but thought it was worth mentioning.