And then, when I unscrewed that Squier '51 neck... horror!
A crack in the neckpocket of the '51... a good thing I took it apart then.
And the cause for the gap in the neck connection was clear as well... the neck was attached to a far thinner body, so the screws were to small and couldn't hold on to the neck to well.
So I bought some longer screws (6cm) and shortened them to 5.5cm.
Now the neck sits firmly in the neckpocket.