Are the online hours for the lighthouse itself or is that for the museum. Does the lighthouse close?

It's for the lighthouse. It is only open during those hours and is not open all the time.

The hours are for the lighthouse and museums. Noon to 4 Memorial Day to Labor Day and lighthouse festival 2nd weekend in October

Property is open til dark, house is only certain hours.

There separate hours and time of year that the light house is open. The other building there has different hours too. Neither is open year round.

You can walk through the park even if the lighthouse is closed.