To my limited knowledge, you do not have to be a resident to get a golf cart permit. I wasn't when I got mine, but trust me, you will be spending half, if not more, of your vacation in frustration going through the process. You have to obtain a Belize driver's license and then..........."don't stop the carnival" begins. Don't know how it is now, but it was that way when I got my golf car permit about four years ago. Made at least a dozen or so trips to the permit office and that's when they were located in the DFC area....hell you needed a Cat D5 to travel those roads back then.
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I'm happier than a pig in s__t...a foot on the sand...and a Belikin in my hand!