I had the same problem, it slowly got worse and one day it did not engage at all. I then gave the starter a light tap with the shaft of a hammer and it started but then stayed engaged so I had to disconnect the battery to stop it.
I think the problem is as simple as lack of lubrication of the starter mechanism, so it might be possible to fix it once you got the starter out. I have never tried it though, as they are not that expensive.
It can be bad contact in the solenoid, or wear out brushes. Slight chance it could be ignition switch.
Years ago I was able to buy those parts separately and rebuild starter for low cost, now you have to buy whole thing I am afraid.
If it were me, I'd check the condition of your battery. You need 12.4v at rest for a fully charged battery. With the car running, you need no less than 13.4v at the battery terminals. If you have less than 13.4v, the voltage regulator is most likely failing.
The VR is easy to replace and no expensive. Usually less than $30 from online sources, approx $40 at NAPA. It is located on the back of the alternator and held in place by two phillips screws. Takes about 15-20 min. to change out.
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