I've never heard of doing that before for fish, but I know some people swear by leaving a tv or something like that on for dogs or cats, so if other things have not helped, and you think it would help, I'd say give it try and see what happens. For the first time, maybe try it out when you are out for a shorter amount of time, as opposed to many hours, so if it doesn't work or makes him more stressed (although I doubt it would) you'll be back soon after leaving, and you can try something else, if you'd like.
Does he have a permanent place to hide that he likes to use? Like a cave, log, ceramic pot, bushy plant, etc. because maybe he feels fine when you are home (even if you are sleeping) but feels insecure or stressed when you are gone and would like to hide till your return, but can't because he doesn't have a hiding place he likes. You could try adding more hiding places. Some bettas really like those floating betta logs.
You could try a ping pong ball to keep him distracted from biting his tail. Also, based on what I've read on these forums, some bettas seem to like having a "friend" in the tank, like a snail, african dwarf frog, or some other compatible fish but that really depends on your Betty's personality and of course Tank Size! If you've only got a small tank, that really limits or in some cases completely eliminates your options as far as other tank inhabitants go. Some, most certainly not all, seem to like having another betta in a separate tank next to them, but other bettas find this totally stressful. If a "friend" or "neighbor" is not an option due to small tank size, limited space, your betta's personality etc. just keep doing what you're doing, maybe try leaving tv or music on when you are gone, and making sure to interact with home when you are home.