The 'way in' to sealed square shafted selector switches is often,
as you have discovered, the gap around the shaft. Decent switch
cleaner / lubricant seems to have good creep and penetration
characteristics, and a good squirt up the shaft gap, will, in most
cases, find its way into the switch body, and do a decent job
of restoring contact.

These were not that type switch (they're pushbuttons), but I appreciate the
insight.