Character head does not animate

I have a rigged character that I'm uploading to Mixamo and it's 99% working and animations are playing correctly, except that the head of the character isn't animated as if he has a neckbrace on.

I've attached a video of what that looks like too.

This is the skeleton and heirarchy as they appear in Blender:

I got the original rigged model from Sketchfab (The original setup doesn't animate the head either when uploaded). I removed the bones for the sword and the top of the head.

I found this post on the forums detailing the same problem and the solution there was to uncheck "NLA Strips" and "All Actions" in Blender when exporting the model. I tried that and it didn't work either.

If someone could point me to what needs to be changed, whether there's a problem with the armature setup in Blender or an export setting I need to change etc, I would be immensely grateful.

Thank you!