solenoid? cables? dirty starter shaft?

[beckoning]

'89 Merc 100hp runs like a charm. No saltwater use ever, Lake Michigan only. Dual battery system (each 12.7v) through Perko switch installed 6 yrs ago. For past 2 years, 50% of the time, starter just Whirrrrrrrs without engaging on the flywheel. If I try it a few more times, it will finally engage. Or, if I turn Perko to "both" it will usually engage. Seems to happen in cooler weather rather than warmer weather. Luckily, when 2-3 miles out after trolling, it eventually starts from the starting battery that I had isolated on the Perko after running out to fishing spot, thus giving the start battery a good charge. I use deep cycle for electronics while trolling. The starter and Bendix spring seem to function OK. Is this a solenoid problem? A battery cable connection problem? A sticky/dry starter shaft? Something else? The solenoid seems readily accessible and probably easily available.

Your ideas would be very helpful. Thanks in advance.