If I as a US citizen become a part owner of a Belizean business ( say 10% ownership) where my business partner is Belizean can I work at this business?
Yes, if you have a work permit, or your residency.
Note that there is a section on the Belize Insider website that gives you information about working in your own business. Here is the link: https://internationalliving.com/country_clubs/belize-insider/doing-business/. You can find this on the front page of the BElize Insider website. Scroll down to the Business section, then read that section. You will need a self-employment work permit.