25 yamaha 4 stroke, and many others, do not have electric "choke". They have prime start. The way it works is very similar to an ATV carburetor's prime start (aka choke). A passageway in the body of the carburetor is closed off by the plunger built into the prime start assembly. A cold prime start, the plunger is "up" (sucked into the prime start body). This opens up the passages to allow extra air and fuel into a cold engine. Once the engine is running, the generator supplies voltage to the 2 wires of the prime start, which warms it up. As it warms up, the plunger "drops" back down into the carb body, which closes off the enrichment passages.
To test it: Remove it, and remove it from the two wires. Stick it in the freezer for an hour or so. Then pull it out, and quickly measure the length of the plunger, measured from the base of the prime start body to the end of the plunger (not the needle). Then put the plunger out in the sun for a while. It should extend. How much? There really isn't a specification. It just needs to extend. I've never seen one fail, so I can't say how they "usually" die.
Most commonly, the engine gets hard to start when cold, but once hot, it fires up just fine. That is usually a function of the passageway inside the bowl of the carburetor becoming plugged. Same passageway also feeds the accelerator pump, so a quick blip of the throttle will usually result in a bog or sometimes a backfire. If the bowl passage is plugged, it won't allow the prime start to enrich the mixture, effectively "not choking" it-but the air passage will be open so then it's hard to start. The passage in the bowl has a restriction in it. If you flip the carb upside down and study it, you'll see where the restriction is. Follow the drilled passages, at the end of it you'll find a brass "ball" pressed into the bowl. It has to be drilled out to get to the restriction and the passages that need to be clean. Once clean, you'll have to devise a way for the passage to be sealed back up. A 8mm long 5mm flange bolt with a 5mm aluminum sealing washer works well, but it also entails tapping the threads into the bowl. If you get a crew that's too long, it'll block the intersecting passage and your "choke" and accel pump will not work. Cleaning the passage is tedious. My eyes are not good enough to do it anymore without aid of a magnifying glass or something similar.
Don't want to go through that? Replace the bowl. Its the only other way to do it, and honestly is the best way to do it. But it's not cheap. Be advised that the bowl of the manual start motors is different than the electric start motors, so be armed with that info if you have to replace it. Easier to just use the motor's model number (eg F25ESHA or F25MSA, etc)
If you have to go into the bowl, replace the bowl gasket (old one gets flat and will not seal properly). Also replace the float valve assembly as the new ones are more resistent to todays garbage fuel. Keep in mind that when replacing the float valve, you'll also have to replace the little plastic "pin" that's pressed into the float valve itself, as it's not reusable from the old one. It just pushes in with finger pressure but make sure to lightly lubricate it before pushing it in.
2001 may have had the old style carb, which was non-adjustable. When servicing one of these, under the top cover there is a tiny jet with o-ring that tend to fall out. They are about the size of a ball point pen's tip, tiny, and easy to not see them. If you blow it out and the jet/o-ring fly away, they are gone forever, and you can figure on a $20 mistake. Please don't ask me how I know..
If you had to replace the carb, get one for a 2005 or newer as they have adjustable idle mixture screw. The earlier ones did not. The newer ones, the screw can be removed (cap has to be drilled out to gain access to it), and then that passage can be cleaned. And the main benefit is obviously that the idle can be tuned MUCH better instead of just a little too lean.