All advice you are getting is correct. It may be confusing because there are three switches controlling the pump:
*there is a breaker on a panel with other breakers on the forward bulkhead of the engine room. This powers the pump, and when the breaker is open (green button is “out” like when you trip a breaker with the red button), there is no power to the pump.
*On the 24v panel the switch has two positions. When switch is ON (MANUAL) the pump runs continuously. When in the AUTO position, the float switch controls the pump.
*On the pipe coming up from the sump is the Float Switch. It is controlled by a string that turns the pump on when the sump fills enough to float the piston up enough to turn the switch on, and when the pump removes enough water from the sump, the string pulls on the float switch and turns the pump off. My float switch failed in the off mode, the pump wouldn’t run in AUTO mode. Another time the string became fouled and prevented the float piston from falling as water level went down, so the pump didn’t turn off.
You can determine if the AUTO mode is working properly by moving the Float Switch with your fingers. Check that the string moves freely as the float goes up and down, and that the switch turns on and off as the float goes up and down.
Everything seems to be working properly, but the sump isn’t emptying, check for leaks in the intake hose (most likely a fitting, but could be the hose itself given your boat is 24y old). While you have it out, check the one-way flapper valve at the bottom of the intake hose.
While you are working at the sump, clean the sump and hoses and float switch mechanism, and make sure the bonding strap is intact. (It is a copper strap connecting the bonding system to a keel bolt at the bottom of the sump, and is important to prevent galvanic corrosion of the keel.) A wet/dry vacuum will get the last bit of water out so you can see the bolt.
If the intake hose has no leaks, you will have to take the pump apart to find why the pump isn’t working. As Alexandre’s and Danny’s posts say, it’s most likely a flapper valve, the plastic part that moves the diaphragm up and down, or the diaphragm itself.
Let us know what you find.