Decide whether the climb is right for everyone
The Texas Historical Commission's visit guide describes the keeper's cottage exhibits and a climb to the lighthouse's viewing area when weather allows. This is in Port Isabel, across the causeway from South Padre Island.
Two ways to make the stop work
Choose the tower if everyone meets the restrictions and is comfortable with stairs. Otherwise ask about the cottage and ground-level visit before setting out. Keep a shared meeting point if the group splits between climbing and staying below.
Pair it with the Port Isabel Historical Museum after confirming museum hours. That puts two history stops on the same side of the causeway, instead of making separate crossings for each.