I live in port a, and fish the jetty nearly every day (that i am home) for tarpon. There is no set location, i have seen them end to end, inside and outside of the south jetty.
Since i primarily fly-fish, i don't cast unless i see fish, then blind cast, or stork and wait for one to feed nearby. North jetty is the same, though i don't take the jetty boat over there ever, but when i don;t need exercise i'll take the skiff out and fish both jetties.
There are no rules, but here are some guidlines:
1) moving water is better then slack.
2) early morning or late evening is better than full daylight, though a good percentage of my tarpon have been caught late morning.
3) When i lived in south texas (south padre) i would fish the jetty at night. Have not bothered to do that here as i get plenty during the day. I seldom hook a fish here as big as the smallest i ever jumped in south padre fishing at night.