A lot of the old literature seemed to mention dry sinew being put straight into the warm glue. Unless you are really strict with your glue temperature the increased soaking time can destroy the sinew with a long soak if the glue is even a tiny bit too hot.
Having your glue a little bit thick and using damp sinew is a bit safer. The slight dampness and the thicker glue combines to make things just right and saves you the bother of adding a splash of water to the glue periodically.
Gaps and bumps are no concern if you wrap and re-heat. It all gets squeezed down and melded together. I have even experimented with using really irregular strands and just slapped it on with no finesse and it comes out looking great if wrapped and warmed.