You are making this far more complicated than need be. If a person is in Belize and conducts business by computer, telephone or any other means that does not either involve products or services originating in Belize or bringing products or services into Belize, they are not subject to needing any permits from Belize.
Example: if an executive of a US company vacations in Belize and telephones or communicates via computer concerning his business, he certainly does not need a work permit.
The determining factor is where the commerce takes place, not where the individual is located.