Fletch Tite, Duco Cement, or whatever other fletching glue you have on hand will do nicely. You might also try coating the wraps with whatever finish you are using on the arrows. I would imagine that just about any modern glue would do the job. Just pick one that goes on thin and dries clear (like super glue).
As far as primitive approaches, I have used spirit varnish to seal sinew wraps, and it does take a LONG time to dry. Could have something to do with how I made the varnish, but I don't know. Plus, it wore off rather quickly. What I do now is use warm hide glue (knox gelatin) to seal the sinew wraps. It dries faster, dries hard, and doesn't wear off like the spirit varnish did, because it penetrates the sinew and binds it all together very nicely. It only gets tacky if it gets wet, which is where a coat of oil, grease, wax, or modern glue would be helpful.