Update

I've added a ‘v2’ model of the top that requires absolutely no glue for assembly.  Instead the dome and the shaft are threaded.  I printed it at .16mm layer height and the threads work well.  Both the top and the bottom of the shaft have a built in 12mm nut.  You can use a box or open end wrench to install it for the first time.  After which I've found you can loosen/tighten it by hand.  Using a higher infill for the dome (~25%) makes the tops movement less sporadic and it lasts longer.  Generally, with 25% infill I get about 90 seconds of spinning.  With 100% infill I’ve had up to 220 seconds of spin time..  I've also included a second handle choice with different ‘wood grain’ look.

This is a recreation of a pull string top from my childhood.  It has a bare wood handle with with a painted and sectioned ‘dome’.  In recreating this I was looking to make it look authentic, but I also wanted to add some fun customization options.

So, the handle includes some texture meant to simulate wood grain.  It's not perfect, but I think it looks pretty good.  The shaft of the top is split into two pieces for a couple of reasons.  First, it's easier to print without supports and second, this allows you to further tweak and customize it with different colors if you choose.  A complete shaft stl is also included here.  I found it difficult to print without wobble, which resulted in failed prints.  Beyond the four printed parts, you'll need a string.  My original top came with a shoe lace, which I believe is optimal because the rigid ends are great for threading and provide ideal tension when pulling the string.

Assembling the top is really easy if you print both portions of the shaft on the flattest surface.  I used super glue to first glue in the top part of the shaft, followed by gluing the bottom portion to the top portion.  As long as you give it sufficient time to dry it should hold with no problems.