What's the right tape to use on split loom tubing?

Decent electrical tape will work. So not the 10-rolls for a dollar kind you'll find at the big box stores.

If you want a fully waterproof solution, the recommended tape is self-amalgamating tape, but even that has to be covered with PVC tape. (note that I've never used self-amalgamating tape, and the wheels have never fallen of a car I've worked on yet..)