The grommet in the stick is coated with "something" and, considering how good of condition it appears to be in 25 years later, including god knows how many years in a barn, I'm guessing it has some property that helps preserve the rubber. Silicon sounds like as likely a candidate as any to me, so I think I'm going to go with that.
And I know nothing I do will protect it against flexion, I'm just looking to prevent excessive cracking from it drying out. Considering the source I found for them charges $25 and doesn't look anything like the one in my stick, I'm going to not go with the "keep a couple of spares" idea. If you know of a source that has ones that match up to the original and charge $10 or less a piece, I'd strongly consider that idea, as well. And then I'd be asking how to keep them from drying out while I'm waiting to use them....oh wait...silicon...