No, it is not the brushes that are worn out. They are positively fine. I wonder though if I have ruined the pump by testing it without paying attention to the polarity… I noticed there is a single electronic component residing in the area, a diode.
When I put 12V over the terminals, all I get is a faint spark and not a running pump. Trying the pumps (I actually have three!) in the vehicle, they instantly blow the fuse when I connect them.