The lighthouse is in a state park. Generally, metal detecting is allowed on the beach between the high water mark and the toe of the dune. There are exceptions to this general rule.
The use of metal detectors is prohibited on all state park lands, except for coastal parks in the beach zone between the high water mark and toe of the dune. However, park managers have the authority at coastal state parks to further restrict the use of metal detectors and prohibit their use on the beach. Basically, it's up to the park manager on duty. I only detect one state park with a beach and I know the manager so I couldn't tell you about Bill Baggs park. That being said, there are a couple guys on youtube posting videos at Bill Baggs, maybe that is what you are referring too when you mentioned the lighthouse?