If I had to guess, I would say that spring would be the best time to see any bioluminescent algae in the Gulf of Mexico. I’m not familiar with the area, but spring turnover releases nutrients that are usually unavailable to surface waters and allows a bloom of growth for phytoplankton around April/May.
Most animals bioluminesce through the use of proteins. A chemical reaction between luciferin and and luciferase releases energy in the form of light. Many animals that have bioluminescent spots achieve this by “enslaving” bacteria that naturally glow. Other animals, like fireflies, do this chemical reaction on their own.