FWIW, for my small medicine pouch suspended from my neck back in the 70's, at first I used artificial sinew because I could not get real sinew. That turned out to be a dumb idea as it sort of sawed into my neck.
Then I used a single, small buckskin lace I cut from buckskin in what the old Herter's Catalog called the "babiche" method. That meant to take a sort of round piece of soft tanned buckskin and cut lace from it in ever smaller circles around the circumference of the leather piece. That was plenty secure and far more comfortable on the neck. However in those days, real brain tanned buckskin was very hard to get and most of us used the non period correct modern tanned buckskin.
If I were to do it today, I would try to use real brain tanned buckskin or at least the "German Tan" buckskin that Crazy Crow sells and still use a single, small lace just big enough to be secure to hold whatever size neck bag/pouch I was making. That could also be used for some jewelry or stones hung from the neck.
Gus