I was just up on our roof and noticed a 2 inch jagged gash in one of
our 3 tab shingles. The gash seems to go through both the top shingle
and the one below it. We have not however noticed any leaking (yet).

The shingles are old and I don't have any spares and am not sure
how/if I could match them anyway. So, I was wondering is there any
reasonable way to patch the gash.

One possibility I was thinking about was to apply a couple of layers
of tar paper to back of the shingle attaching either with epoxy or
with the black gutter caulking. This would hopefully keep the sides of
the gash aligned and fill in any gaps in between - I would probably
also add a bead of the black gutter caulk to fill the gash from the
front side too.

Any suggestions/comments?