what does" out-of-time feel"mean?
While he considered himself an avowed urbanite, he liked the quiet of the village, the middle-of-the-night Brigadoon feel to it with every-thing shut down, closed up, and the sound of waves rumbling nearby.
A few fingers of ground fog crawled in, adding to the otherworldly atmosphere. The storm had passed, but it left the air thick with wet, and the sky too heavy to show the moon.
The flick and flash of the lighthouse on the point added to the out-of-time feel. He headed toward it, using the time to decide just how to handle the situation.

Question

what does" out-of-time feel"mean?
While he considered himself an avowed urbanite, he liked the quiet of the village, the middle-of-the-night Brigadoon feel to it with every-thing shut down, closed up, and the sound of waves rumbling nearby. 
A few fingers of ground fog crawled in, adding to the otherworldly atmosphere. The storm had passed, but it left the air thick with wet, and the sky too heavy to show the moon. 
The flick and flash of the lighthouse on the point added to the out-of-time feel. He headed toward it, using the time to decide just how to handle the situation.

Answer

He feels as if he's in another dimension where time moves at a slower pace. He feels somehow separate from the rest of the world. It relates to the reference to Brigadoon earlier in the paragraph. Brigadoon was the name of a musical of the time period about a Scottish town that appeared for a day once every hundred years, so time progressed much more slowly there than in the real world.