Lee, welcome to the club. The damage doesn't look all that bad - I've certainly seen worse and the pickup still worked. The easiest way to test it is to swap it with the neck pickup and see if the trouble stays in the bridge circuit or migrates to the neck circuit along with the pickup. Unless someone has been messing around with the electronics, you should be able to just unplug the pickups (solderless), to try the swap. (you don't have to physically move the pickups, just swap the leads and see if the one that doesn't work comes back to life and vice versa.
Bill, the guitar one