Just from the symptoms sounds very similar on an old vette. Every 6 months the big neg stud and spring loaded copper spinning disc (both in the solenoid) would need sanding smooth from arching/corrosion. Not certain the design is the same as in '69 though. Another time very sim symptoms again with a boat and a brush bolt simply backed.
I'd just pop the starter off and dissect it for pure curiosity. Check all your wiring connections first of course - corroded - cut insulation.....
\'96SS SOB: SSRI, Herter Tune, Tri-Y II, , 3000 Edge, F/HO bars, METCO extendeds with CV MMC, Bilsteins, currently Vredestein Ultrac Sessanta (315/35 rear). Finally, wait for it... LT-4 knock module!
\'96FWB BUW-Butt Ugly White: PCMPerformance tune, HDFA w/ swissed filter, 1/2 SLP s.s. catback with H- and Flow Super 50s, oem opti rebuilt 3 times, SS Bars, METCO LCA, Airlift 1000, Monroe SS, PowerTrax No-Slip, CTS wheels with +1 rubber. Finally, yes again... LT-4 knock module!