It appears as though mine has decided to run 24/7. Anything it could
be that I might be able to take care of on my own, or should I just
bite the bullet and call for a plumber.

Fix or replace the switch.

First, check to see that the float is not just gummed up with tree
roots or mud or whatever. Have you checked to see if it still floats or
sinks with the water level, and won't shut off even with the float
hanging down?