I'd be curious about the same. My boat is in Belize (just sailed in two weeks ago) and will be there until June. I'm working my way to Costa Rico for an indeterminate stay. Though I didn't ask the specific question, both customs and immigration were aware of our intended length of stay in Belize and no mention or request to pay any tax was made by the authorities.
I'm interested in discussing the safety concerns related to to the Roatan to Panama (off the coast of Nicaragua). Are you taking the same route?