If I worry that the duct tape is going to let go 65' up the mast, I sew the two lines together with a sail needle and waxed twine.
The above way is much preferable over the duct tape method. That is unless you have other work for the rigger to do when you hire him to go aloft to fish the new halyard through the mast after the tape comes apart when you get the junction to the mast head and attempt to pull it over the sheave.
Trust me. Butt the ends together and stitch them.