He sat very still while on the branch, and stayed on the branch for a long time. He flew off once and went out of sight near the cliff. (Nothing remarkable about the way he flew.) He returned after a short time, and sat on the same tree, different branch. In all I probably watched him for 20-30 minutes. He didn't fidget and didn't move his tail.
All of the Eastern Phoebe descriptions I found mentioned tail bobbing.
I agree with Eastern Phoebe. We've had some here who do not bob their tails. The lack of an eyering, faded wingbars rule out other flycatchers. Juveniles will show a yellow-ish belly and the adults will in the fall.