We have several ~55G plastic (almost nylon-ish?) barrels in which
we collect rainwater. They were originally used to hold detergent
or bleach or some other agent used to wash clothing, linens, etc.
(rescued from a local hospital's "laundry" as they are routinely
discarded, intact).

Most recent rainfall filled them all, again (I'd assumed we were
*done* for the year -- though I've assumed that for each of
the last three storms! : )

But, one barrel obviously has a leak. Over time, it's now down
to just a few inches in the bottom of the barrel. So, we know
the leak is at or below the current water level. I don't imagine
any *other* leaks are present as I'd been "feeling" the exterior
sides for signs of moisture and never found any.

I *suspect* the leak is inthe actual bottom end of the barrel;
the reason it has slowed/stopped is possibly because the leak is
fine enough that hydrostatic pressure at this low level is just
not enough to push much water out through the crack (recall any
sediments in the water will tend to want to *fill* the crack
thus further impeding flow).

As the suspected location is on the bottom, the only approach I can
think of to locate that would be to elevate the barrel on an
"open frame", keep it level (so water comes out from the crack and
doesn't cling to the underside of the barrel to find another
path to ground) and fill it with water -- perhaps even putting
some color in the water (e.g., Miracle Grow would give it a bright
blue color and not be inconsistent with the intended use of that
water -- if I never managed to clean the MG out, completely).

[The barrel has an open mouth so I can't just "plug up the inlet"
and pressure test it]

Any other suggestions to locate the leak?

Is caulking compound (on the interior) likely to be a permanent solution?
Or, an epoxy? Or, just toss the barrel (we'd have to wait for a biannual
special pickup to discard something of this size -- unless I dragged
out a sawzall and diced it up!) and go pick up another from the laundry??
(which is also tedious as they are large and have remnants of nasty
liquids in them before you get them home and clean them)