Is the owner aware of the problem? How long from departure to reactions?
I like to find "break points" for a dog and work from there. If the dog is fine for 15 minutes then starts, have th owner go for 10 minutes and return BEFORE the dog reacts. You know the drill about re-entering the home and no attention for 5 minutes. Repeat (many times) then start adding 1 minute more... repeat.... I *believe* that once your pas the 20 minute mark you can up the anti by 5 minute markers.
My guess is, that if the dog is taking a while to react, it's more boredom related and i highly agree with the kong suggestion. Stuff it, freeze it... give the dog a job. In my opinion a border collie is a highly intelligent and mother nature programmed them to be inter-dependent on human relationships. Being alone is a tough thing for this dog I'd bet. Add to that the past he has and his behaviour is perfectly reasonable.These dogs were meant to herd all day long, running, thinking, working. An afternoon on a veranda, most likely is not cutting it!
One of those balls that you fill with kibble and they have to roll it around to get their food is another time occupier. A plastic pool filled with water and his toys floating in it.... once that gets old, fill it with sand and bury the toys. Hiding the toys under a beach towel may give the dog something to think about.
Either way, separation anxiety or boredom, the problem will not go away on its own.