I repaired mine for this DISMeet trip and used a JB Weld product from Lowe's that had two different tubes that you mix together and then smear on the joint (it will run as it is liquidy at first). But I too used the painter tape to hold both in place (I did one ear at a time).
The issue I ran into is that the big globe head made from a different material than the ears (the globe head was shiny and stiff, the ears more plasticy. Some glues are good for one and not the other. But the stuff I used worked well enough.
Best is to treat the globe head/ears, once they are repaired, with kid gloves while storing, transporting, and using.
Ed
PS - the Loctite product in the picture above is what I used when I built the lamp initially but it was no longer in stock at my local Home Depot or Lowe's. So I had to use an alternative as noted above.