If you have a South African degree in Optometry. B.Optom. Can you work legally at any optical shop in Taiwan. Does Taiwan accept the degree?

Maybe if you have an OWP or a JFRV and your Chinese is good enough and you could persuade someone to employ you.
As for getting a normal employer-sponsored work permit, I doubt very much if this would be allowed. I think you could find a list of approved job categories for foreigners from the Ministry of Foreign Affairs. I’d try that first. But I’d be surprised if the people working in those shops from 11 in the morning till 10 at night earn more than about NT$20,000-NT$30,000 per month.