I've made a really unusual character - microphone whose stand has two "necks" that attach to the head. (See below) Only the right neck will attach and move properly to the head of the microphone. Both are tagged as necks and independent. Any work arounds here would be amazing.
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In general the Neck tag is only used for a few behaviors like Walk, so I don't think your character actually needs it. More important seems to be where the origin of the main "Head" group is, which serves as the primary place where the head will pivot from.
It may make sense to add a bar in the body that connects the two curved side pieces at the top, but is hidden by being blocked by the head. That would give the head one central point to attach to, and would be a good place probably to put the head origin.