No traffic lights sounds relaxing and mostly is, but it has consequences. Junctions on Periwinkle Way are four-way stops and roundabout-free, which works well at low volume and less well when the island fills.
The pinch points are predictable. Saturday is changeover day for weekly rentals and the eastern end of Periwinkle Way, where causeway traffic arrives, backs up in both directions in the middle of the day. January to April is the high season generally, and the hour before sunset pushes traffic west towards the beaches.
Speed limits are low and enforced, and the island has a great deal of cycle and pedestrian traffic crossing the road between plazas and the path. Wildlife crosses too — this is an island where a gopher tortoise on the tarmac is a normal occurrence rather than an event.
If you are staying on the island, the honest advice is to park the car for the week. Between the shared-use path and the compactness of the commercial strip, most visitors find they use the car for the grocery run and the trip to Bowman's Beach and nothing else.