I have a rescue gelding (gelded in his 20's) that did it non-stop when Spirit was here. There was a 16' alley between their pastures, but he just couldn't stand having that "competition" across the way. Once Spirit left for Julie's, he calmed down.
He now shares a fenceline with younger in tact males and a gelding but he pays them no attention because they are young, he has all the girls and they aren't a threat to him.
I have had him several years now and he's in the best physical and emotional shape now than I've seen him. If I brought another mature stallion home, which there are no plans to do, it would probably kill him at his age.
Can you give your boy a mare or even try a young gelding or colt as a pasture mate? Just be careful with the introduction until you know if he's the type that will live peacefully with another male. If he's never done it before, he may not accept a young male as a non-threat.
Good luck.