Undercut the top and taper it about the same as the bottom of the icicle base. Sand and finish.
Taper the piece to a peak. It does not need to be any more than 1/2" to 3/4" deep in my thinking but your design may again vary.
Here I have cut a couple of decorative lines and dimpled the center with the point of the skew. Dimpling the center will make it much easier to drill for the screw eye later.
The top can be drilled for a screw eye while on the wood lathe, however, I refer to move it to the drill press, hold it in a jig I first made for drilling pen blanks and now use for lots of small holding jobs, and drill a 1/16" hole there.