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Most of the people with advice on this subject are not even mechanically inclined.
I don't know most of the people with advice on this thread but I know some of them cannot resist the urge to take something apart, scatter it all over the driveway, screw up something else and then put it back together.
I know another few of us wouldn't exert the effort to try and fix something that is marginal like that, just to say we did it. Better to wait until there is a reason to go to all the trouble to pull the transmission than pull it to fix something piddling like a balky synchro.
2020 Corvette of the Year Finalist (appearance mods)
C1 of Year Finalist (appearance mods) 2019
I'd first change the oil to good ol dino 80-90 weight lube. Someone MIGHT have put synthetic in it thinking that was better.....it's not.
And check the linkages when you're under there. Take off the tranny levers, put a pin through the shifter in the neutral position and make sure the trans is in neutral and then check to make sure the rods are exactly the right length.
I'll add that for you, snoopy, a mechanic of 50 years experience, the best move would be a teardown and inspection. A lot of folks on this forum would take that advice, and the trans would be scattered to the four winds and the car would sit in the garage under a tarp for the next 20 years. For these folks, sometimes it's best to leave well enough alone. There are guys on this forum who are meticulous AND skilled, and are able to rip apart and rebuild anything on these cars. There are many folks who just happen to love old Corvettes, but are better off not fiddling with them in too much depth. Most professional mechanics take a 'tear it out and fix it' attitude, but not everybody should take that path, unless they are thoroughly prepared for the possible consequences. Welcome to the Inner Circle.