Re: 1987 125 Force shifting issue
If the pump housing was that badly corroded, you also need to check the walls of the lower plate. That's the plate held on by an additional three screws--one in the front and two in the back. There is a center wall in this plate below the stainless plate and gasket. If this wall is corroded enough that it does not seal against the gasket, it will short circuit water from the outlet side to the inlet side of the pump. This can reduce efficiency enough that the engine may overheat even with a new impeller.
This torpedo shaped plate also carries the drive shaft seal and the shift rod seal.
Sometimes with age the shift rod seal will swell and tighten on the rod OR with improper installation, it will be too tight resulting in the engine being able to shift because of the leverage in the system YET, you can not move the shift rod by hand. If this is the case rather than the dogs hitting each other, then remove the plate , remove the old seal and reinstall a new one--it only costs 8 bucks. It is installed steel side up, rubber side down. You press (hammer) it in using a suitable sized socket and a piece of pipe (Because you install it with the plate on the lower unit and the shift rod in place). It should be snug enough to seal out water yet the rod should slide smoothly through it. So start a little loose and continue to tap it in until you get to the correct compression. As I said, you should feel a little drag when moving it by hand but it should not be excessive and it should be smooth You should be able to move the rod by pinching it between two fingers with moderate pressure--anything more than that is too tight. If you got it too loose and it leaks a little water, you can always tap it in a little tighter.
The drive shaft seal is either 17 or 27 bucks and if you need to replace the plate, you must use a new seal as you can not remove the old one without damaging it. Even if the old plate is OK, It might be a wise move to replace the seal anyway.