I recently came into an old Singer treadle sewing machine. Most of
the veneer is in fair to good shape, but is delaminating to various
degrees from almost all the way off to just the edges being loose.

I am seriously contemplating refinishing it (as opposed to using the
base for a hall table).

Anyone want to give me some suggestions on re-gluing, especially those
barely loose pieces, with only a 1/16" gap or less to get glue into?

TIA
Bill

I had the same problem with my grandmother's 100+ year old Singer. You
could try to use a glue syringe to inject glue. In my case the veneer was
to far gone to reglue and I had to replace the veneer. I use white oak PSA
veneer from Van Dykes and mixed several colors of stain to match the rest of
the cabinet. You have completely disassemble the cabinet to take the top
apart. Once the top was disassembled, it was fairly easy to clean up and
apply the new veneer. It is usually moisture and/or direct sunlight that
causes the old hide glue to fail. Good luck
Scott