I believe it closes about 2 hours after AK closes. We ate there after AK one night and there were special busses there to take us back to our resort. It seemed to me it was around 7:00 when we left and it was almost empty.
Make sure you call the RFC and confirm the time that they close. We had dinner ressies there last summer and when I made them I was told that they closed one hour after the park closed. We drove all the way out there from the BWV and found out that they closed the restaurant the same time as the park. I talked to the manager and he told me that it was slow at the AK that day and they decided to close early. He was very apologetic but we were a party of nine and I knew we would not be able to find anywhere else to eat. He was able to call the DTD RFC and get us a table there with no wait.
They aren't going to kick you out when the park closes but you will not get in after the park closes either. When I made my ADR I wanted 5:30 or something and was told I had to take 5:00 because that was when the park closes that night.
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