My 62 and my 64 NOS both have very stable necks. My 62 is a 1988 model, so I'm not sure if it's the age or better woods but the neck never moves.
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Same here. I've never had to adjust the neck on my 2008 '62 AVRI Jazz. The neck is perfect on that one, perfect string height all the way up the neck, perfect frets, and it never moves.