It looks like the Seaport Market Jumbo Turkey Legs kiosk is operating seasonally — it's usually open in the summer, when the park is at it's busiest. It's worth noting, that even in the winter/holiday period when the park is also busy, Seaport Market has not (in recent history) been open. All of the larger logos and names have been taken off the building, and small A-frame boards are brought out when the location is open.

Turkey Legs can be found over at the Waterway Grill/Bar location, on a more regular basis. So if you really want a turkey leg and Seaport isn't open, they may be able to get you one over at the Waterway Grill/Bar.

The Seaport Market location is a bit to the right (south) of Seaport Pizza (which is also only occasionally open). There are a few umbrella covered seats nearby at Seaport, but we see quite a few people just walking around with the turkey legs.