How do I repair a split in trim boards?
I think you're on the right track.  I'd apply enough glue so some squeezes out, wipe the face with a damp towel to remove the residue, and either clamp it or wrap it with blue painters tape until dry.  Just make sure that the wood remains flat and not bowed when you clamp it.  After the joint is dry, remove the tape or clamps, and you should be good to go.  If the finish is hazy, polish it with steel wool (0000) or I'd use a rattle can of poly or Deft wood finish to feather it in before you install it. It will take another 10 minutes and better disguise the split.  If it's a dark finish, there's "dark wood" Titebond available.