You traced the etymology yourself - you're using it as a variant modern self-created spelling of Giles so 'young goat, kid' would still be the meaning. There is no other etymology because, simply put, if you distance it from Giles, it's simply a name you made up and names you make up don't have linguistic meanings unless you based them on a word or another name.
I haven't seen Jyle but there's a woman on the opinion board who has a Jye.
cheers
Devon