Looking at that inertia starter. It would not be too bad to disassemble although, the starter pinion has to come off and that retaining ring is a pain to get off. Two things could be wrong either starter pinion fiction pad is worn out or the top motor bushing is worn out. Pinion and starter repair kit for pinion replacement are available but the bushing is not. I see quite a few Kohler starters with both of these issues. Most times the pinion fiction is the reason the pinion doesn't moves up. Where the bushing usually causes a dragging motor. If you taking the main motor apart just be careful of the brush springs popping out.
I just took a Denso solenoid shift starter apart this week without a manual and it is back working again. Just take your time and pay attention to the disassembly.
Starter repair kit only contains the following items which are right above the pinion.
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