So the mount is loose! There is a set of nylon washers which wear out so the joints flex. You’ll need to take the mount apart which is a bit of a task! You’ll need a set of special tools from these folks [https://www.mail-archive.com/lemswap@googlegroups.com/msg35722.html|iMac G4 neck disassembly tools (for the proprietary 3-prong screws, custom designed and 3D printed)] if they still have them or you’ll need to make your own.
After taking the neck off and opened up you’ll see the washers. This is the hard part as you’ll need to find something that you can fit in to replace the worn washers.