I try to solidify everything that I know while it's fresh in my mind. I walk to the shot location and mark it. I then walk to the last spot that I saw him, confirm it, and mark it. Then at least I can focus on the ground between the two marks and look for sign, tracks, blood, hair, arrow, etc...
Since you know he is out of sight over the finger ridge, you have no issues tracking to that point. In that distance you should be able to get a good idea of the quality of the hit and whether you should press on or leave him be a little longer.
I mark every piece of sign I find with flagging ribbon. Some folks use TP so they can just leave it, I like flagging ribbon because it's so visible. I just have to pick it up before I leave.
The last time I had to track an animal, I kept losing the trail in one particular area of thick fir saplings. I could back up to the edge, line of sight the ribbons and continue on but never could find sign on the other side. At this point I started circular gridding out in tight circles and within 10' found where he had turned inside the fir trees and went down hill before falling and sliding down off the edge of the cut bank below me.