That is a cool website. I would guess the plane is the one labeled FA7X on this site. Looks like it came from Boeing Field, flew out near Newport on the coast, followed the eclipse path just north of Corvallis out to eastern Oregon, and then back to Boeing Field landing around 10:54am Pacific. It was going fast and at high altitude (about 41,000ft and 430 knots), unlike most of the other planes in the area. Its altitude probably explains why it was the only jet creating a visible contrail. If this was the jet, it shows how bad eye witness testimony can be as it flew almost due east over where I was. The site says its a Dassault Falcon 7X; so a bizjet type plane. No tail number like many other planes shown. A quick google did not get me a list of the planes in and out of Boeing Field that day, but I would imagine it's available somewhere.
Glad you found it. The 7X is popular for eclipse hunters, they can cruise high and stable and have good-sized windows and can take about 18 people with all their kit; they also form their contrail aft of the tail due to the engine location, so less interference for photography.
I have a couple of friends who flew on one over the Faroes during the 2015 eclipse, there were more than a dozen chartered aircraft circling for that one.
