It all depends on how it's wired.
I use that phrase a lot.
You need to trace the wiring and find out how it works.
There are so many variations on the theme:
direct wired to battery, direct wired to battery with a separate switch for manual, off automatic operation, panel mounted switch, which could maybe require the main panel switch to be on, or off, you name it.
Unless YOU know how it's wired, there's not much we can do to help you.
When electrical stuff doesn't work, it's usually one of just a few things: connections, connections, connections, broken wire, or blown fuse. Rarely is it the switch, but that could be it, too.
Much of the bilge pump wiring is in the corrosive atmosphere of the bilge. I have completely rewired our bilge pump three times in the last 13 years. Two or three new pumps and a few new float switches, too.