The 1/8" tubing was a loose-fit into the counterbored 1/16" holes in the back of the nose piece. Used JB-Weld, about half the depth of the cbore, and a fillet around the nose/tube to make a tight seal. Rigid styrofoam. impregnated with epoxy, secured the tubing at the bottom and top of the mast stub, so the tubes won't rattle around in service.
Once the fairing is smoothed out I'll prime the pitot.