How about loose/ dirty connections from battery >to> solenoid >to> starter. And battery >to> ground. Any connection that involves a nut, bolt, screw should not be overlooked, taken apart, cleaned, and tightened well. Pass nothing by, saying: "it looks good".
Your solenoid may also be Internally burned, and the plates within no longer make good, consistent contact. Replace it, if it is the problem, or replace it, as a test. I justify these things as, they have been on here forever (one day it will fail!). This is preventative maintenance, even if it is not my problem. Probably $20.00 or less.
Neutral safety switch may also show the same symptoms.
The Medic
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Sunday, January 5th, 2020 AT 7:48 PM