To me, it's a mystery.
The only thing see of note, if the is the 'T·W' punch is that of Thomas Wallis (I), then it appears to be filed down a little on the right hand side top corner. This may indicate that the punch was starting to show damage, maybe a crack starting to develop, filed down, and then because of its suspected brittle nature, kept as a spare. I should think punches, especially at this time, were expensive items and I doubt TW (I) upon retirement would have destroyed or discarded such pieces and likely would have passed them on to his nephew, TW(II), who of course, has the same initials and may well have used them in a emergency if the need arose.
Another point, what was retirement for 'TW(I)'? He may well have retired from business on his own account, but he may well have "kept his hand in" working in his nephew's business. If so, perhaps he still, as a matter of pride, payment, or whatever, stamped his own work with his own punch. In those days, unless you were wealthy, you worked till you dropped. Just speculating (as usual!).