Re: 25 hp Evinrude won't shut off
The kill switch works by connecting the black/yellow powerpack kill wire to ground. Since you've eliminated the switch it has to be a wiring fault - a nearly open circuit - could be inside the insulation.
Trace the black/yellow back to the powerpack, make sure it' s making good contact inside the plug.
With the engine running, use a jumper wire to connect the ground side of the switch directly to the engine block and push the button. If that kills it, then the problem is with the ground wire.
Unplug the powerpack, push the black/yellow pin out of the connector, plug the pack back in. Check the pin connection to the wire for corrosion & looseness. With the engine running use a jumper wire to connect the kill wire to the engine block. If that works, the problem is between the plug and the switch. If it doesn't it's between the the plug and the powerpack.
good luck.