My cat has a tiny piece of his third eyelid missing as if it was torn
out. The vet is aware of this as she's the one who first told me about
it. But what I failed to ask is if his leaky eye is because of his
third eyelid. He does have herpes but his eye doesn't water like his
sister's. His sister has a nasty, chronic case of herpes that just
won't let up. Her one eye is constantly watery, but her brother's is
more of what I would describe as leaky. It just sort of leaks out the
inner corner of the eye (beside the nose) like a teardrop as opposed to
the whole eye being watery.

Would his damaged third eyelid be causing this chronic leaking?