My cham has an ongoing issue with his right eye. The vet suggested that I get some saline solution from the drug store (just like you use for contact lenses) and regularly flush out his eye. At first I was like "WHAT ???!!" but she said just hold him so his head is pointing down so he doesn't aspirate the saline, then ? ? ? away.
I wasn't so sure of it at first, but he loves it! He wants the drops in his good eye too. He looks up at the bottle and waits for them to drop in his eye.
He will eventually do the cleaning thing with his bad eye, but it takes patients (mine, not his).
I hold him like that until he gulps a few times, then he's good to go!
I attached a picture (it looks really weird) but he wraps his tail around my wrist (that's how I hold him) and sometimes he'll bury his face against my arm and rub his eyes ? it's so sweet!