Actually, I don't think it is "The Vagabonds". It features a saxophone in it + the band formed when Tommy Shaw was only 14 years of age.

https://eu.montgomeryadvertiser.com/story/news/2021/08/05/styxs-tommy-shaw-has-heart-full-music-and-montgomery/8071428002/

http://tommyshaw.net/wp/index.php/biography/