The top of the ornament is thin enough that simply screwing in an eye may split it. In preparation for drilling use an awl to make a center mark for drilling. This awl was made from a screw driver ages ago and has been around the shop for ages. They are quite easy to make for an interesting wood turning project.
Just eyeball the center as it is quite easy to do so after having parted off the top. All that is needed is an indent to keep the drill bit on site while moving into end grain.
These three similar but different icicles have been marked and are ready for drilling. I tend to make these in small baches of five to twenty-five and then drill them all at once. There is usually no rush.
I originally made this jig for holding pen blanks while drilling them. It is easy to duplicate. All I did was take a piece of 2x2 and mark a centerline. Then I drilled appropriately sized holes on center and cut it with a band saw. A small hinge was put on the end and a more comfortable handle fashioned and away we go. One of these days I will make another and photograph the procedure. When I needed something to hold the icicles I took the jig and drilled an a appropriate hole.
I drilled a 1/16" hole about 1/4" deep into the head and with a small pair of pliers I got from the dollar store I fasten a small screw eye in the icicle and attach a hanger. There are other ways to get an eye on the ornament but I got a supple of these small screw eyes a while ago and have not exhausted them yet.
Here are a few ready for the tree. These have been a good seller for me and our own tree has a bunch every year. There are very few measurements involved with these. They are mostly whatever felt good at the time. Use wood with a fairly straight grain and even though they are small, I recommend a face shield as usual. Catches tend to break pieces off and throw them at you. This is good incentive to watch that skew.