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It is also possible that the sticking MAY be caused by the master cylinder, in which case you'll want to check that, too.
FWIW, I change my brake fluid every year. Not a bad idea if you're keeping the bike "forever".
You're no doubt correct. The last time the fluid was probably changed was 2003, when I had new brake lines installed. So ten years and probably a bit of moisture causing the issue. Like I posted, I had noted some squeal earlier this year, but it 'self corrected' over the season. After servicing the bike, and detailing it for storage, it got to the point it is.
I recall having a 1976 Dodge van that had sticky front calipers. Chrysler put Bakelite pistons in the calipers and they would gall and stick. Real MF to service, was cheaper just to go to the store and get a set of rebuilt ones.