When rolls tear on rewind, problems other than old paper might be a
problem.  One thing for sure,  the rewind brake should be completely
disconnected.  ( A loosely rewound roll is far better than a torn roll.
The take-up spool should spin freely and must be  well lubricated.

A very old and fragile roll can be assisted by adding a cardboard ring
made by putting an old cardboard roll core in a lathe and cutting
cardboard rings to fit between the left flange of a roll.  This will save
the left edge; however, it will still allow the roll to wander upon
rewind, and if the roll is not tapped down on it's slotted end the paper
will develop a memory of the wandering and the wandering will get worse.

The tracker mechanism should definitely not be 'on' when the roll is
rewinding.  It could never keep up with the rapid changes.

Bruce Clark