redcows is right on all counts.
If you wouldn't put it in your own eye, don't put it in your cow's eye.
ANY solution/ointment/powder, etc., whether it's oil/petrolatum-based or not, is going to be washed out by normal tear action within 10-15 minutes. If the animal is tearing more than usual - as is the case with pinkeye - contact time is decreased even more.
Long-acting tetracyclines, like LA-200, Tetradure, etc., are the best thing to come down the pike. If given at the appropriate dosage, the tetracycline will be secreted continually in the tear film, constantly bathing the eye with antibiotics.
Never had much success with eye patches on my clients' animals, but if they had me out to treat, or brought the animal to the clinic, I was gonna sew the 3rd eyelid up to the upper lid just to provide some additional support to the cornea and some extra protection. And a whopping big dose of LA-200, with instructions to give another dose in 3 days.