How about this method?
I placed one pen and created a circular pattern (10 instances).
Then exported this model set content as OBJ and re-imported the file to another model set. With the import option, “keep individual parts” was toggled off, so the parts are forced to merge (all tips as one part). This enables to use a gradient (a texture in my case, but a circular fade should work as well). The texture was placed in the middle of the scene and covered all pens.
You can explore the scene. A KeyShot 11 KSP is embedded in the attached ppt. Just open the slide and activate the Object (RMB menu)
pen with gradient tips.ksp.pptx (11.7 MB)
Hope that helps to find a better solution instead of post work.
CheerEO
Marco