I would place a temporary wrap of thread or masking tape each side of the split before attempting the repair. Sometimes a split will run when you open it up with for glueing.

You can use a small coffee stirrer type straw to blow the glue into the seam, just run a small bead over the split blow through the straw to force into the crack.

A few drops of vinegar will thin yellow glues like TiteBond. Use very small drops, it's some kind of chemical reaction, not like adding water to thin, you just need a little.