I love this head scratcher. Went looking at plunger rear brake setups to understand it a bit better. In the picture, the actuating arm seems to be 180 deg out of position. For the appendage to be part of a rear-set brake it would have to be the remains after the pedal portion, which wrapped around the spindle anticlcokwise, broke off. Hard for the likes of me to imagine. On the other hand, it would have been so inefficient that it would, indeed, have been certain to break off.
As for an alternate spring anchor point, I learned that plungers have their return springs at the pedal. (Ah,but everyone else already knew this.) Is it possible that the pedal return spring is not effective enough and some earlier owner saw this as a way to stretch a second spring out to some other anchor, maybe the rear mudguard stay.
Hell, I obviously don't know what it's for, but the challenge of accidentally hitting on something that finds consensus is a lot of fun.
Richard L.