Morning is the reliable choice for most of the year, for three reasons that happen to coincide. The bay holds its overnight calm until the sea breeze arrives, usually in the second half of the morning. The low angle of the light at that hour photographs far better than the flat glare that follows it. And from June through September, storms building inland make an afternoon booking a gamble.
Evening is the atmospheric choice, with the caveats about where the sun actually sets from this island covered above.
Tide matters more than the hour on the clock. Moving water is what concentrates bait, so the productive windows are the middle of a rising or falling tide rather than slack high or slack low. Captains schedule around it, which is why a good operator may offer you an odd-looking departure time rather than a convenient one. Take the odd one.
By season: winter, from December through April, is the island's busiest period and gives comfortable air, low humidity and excellent light, with the caveat that a cold front can put wind on the water for a day or two. Spring is settled and pleasant. Summer is hot and humid with daily storm risk, but the water is warm, calves are about, and early trips are lovely and uncrowded. Autumn is the quietest and, in September and October, the most exposed to tropical weather.
Sunset here shifts by roughly three hours across the year, so an evening departure boards in genuine daylight in December and late into the evening in June. Check the actual time rather than the name of the trip.
