I completely disagree that it is just a young horse thing that they out-grow. If it were, we would not see dozens of questions about what people should do with their 'buddy sour' and 'herd bound' horses. Some outgrow it and others still get lonesome when they are 20. When you have a horse, young or old, that is calling out and lonesome, you have some degree of herd bound behavior. On the low end of this scale are the horses that call out or walk slowly (or weave and stagger like a drunk) when leaving other horses to go it alone. On the other end of the scale are the horses that REFUSE to leave the barn or their buddies. 'Stalling out', rearing, spinning around, etc are on this end of the scale. BUT, most of those horses started out just calling out for other horses when they were ridden alone.
By the time I have put 60 days of training in any horse, I can tell if they have much of a tendency to get super attached to other horses and are going to be a horse that will always tend toward being herd bound and get lonesome.
First, I would tie him out away from any other horses every chance I got. This is by far the best way to teach horses that there is life after separation. You are letting them learn to accept being alone. That wins at least half of the battle.
If I have a young horse like yours, I will bring them along on every trail ride that there is room for them. Then, I tie them out in a safe place while the rest of us ride . As long as they are well accepting of being tied solidly in a safe place, I have never had any problem with it. Most Field Trial horses I know are very well broke for tying. As a matter of face, around here they are all broke to stake out on a long rope.
Once I start riding these horses a lot on the trails, we always separate on every ride. We do the 'leap-frog' thing on all rides. This is where one rider rides out ahead the other stays behind, doing whatever it take to stay quiet and walk. The lead horse rides out of sight at a trot or lope and pull up to a walk well out of sight. When the back horse is quiet and walking right, that horse trots or lopes, passes the first horse and the whole thing is repeated as long as there is time for it or both horses are OK with it. We never ride back to the truck together, either.
When I have ridden a horse long enough that they are pretty good most of the time, I scold them for calling out. I usually do this by saying "Ah!" and take the horse's head away from him making him stand a good with his nose at my leg. If he keeps it up, I will take his head away from him and kick him hard a few times with my inside leg (makes him disengage his hind end). [This is also what I do when I teach a stallion to not nicker.]