Apologies for the quality of the photos. A single bird diving off the beach. Guillemot with winter plummage?
No interactions present.
The blunt, deep bill, and longish tail suggest Razorbill, probably a first-winter. Guillemot has a very dagger-like bill.
My Flickr photos...
Lat/Lng: 56.056, -2.822
OS grid ref: NT489850
Not far from Gullane to the east.