Aaron,
My cat has the exact same thing - one runny eye.  My vet thinks it may be a
clogged tear duct.  She said that a clogged tear duct is not a major
problem, more of a nuisance than anything.  And she assured me that the
pinkish or brownish tinge is not blood (but I can't remember exactly what
she said it was).  The tear duct can be unclogged but only when the cat is
anesthetized.  She suggested that whenever we have to anesthetize my cat for
something else, we can take care of this.  It's not worth putting the cat
under just to correct this.  There is a test your vet can do to determine
whether it is a clogged tear duct if you want to do that.

My cat has had this runny eye thing off and on for about 2 years now - and
he is fine otherwise.  I just wipe his eye whenever I see it running.

Sue

try using Optex....  I used it diluted down with cool boiled water, but my
friend uses it neat... also cod liver oil is good, if you have the capsules
just pierce with a pin and drip in!

Ok, folks listen up.  There is a medicine called Terramycin, and it's for
eye problems in cats (maybe other animals too, not sure).  You could
probably ask your vet, it's about $8.00 for a small tube that is more than
enough for 1 cat. I took my Bear (cat) to the vet and that is what she gave
me and it worked.  Put it in the eye 3 times a day for about a week to 10
days. She said that he had conjunetivitis. A feral cat had kittens under our
house during the same time, the mother cat disappeared so we brought the
kittens in and have been raising them I think they were 3 weeks old when we
brought them in. Everyone of them had the same thing wrong with them some
with just one eye, some had problems with both eyes.  I went onto the net
and purchased extra terramycin and glad I did, it's helped with their eyes
as well.

Hey, anyone want 2 beautiful long haired yellow & white kittens, they are
now litter trained. I'm in Georgia.