Rigged Mesh Behavior Is Different Despite Same Weights In the attached images, I have a mesh that I rigged with automatic weights. The auto-weight turned out pretty good, minus a few tweaks. However I ran into issues with the mouth and eyes.

I applied weights to the teeth and eyes based on the weights of the nearest vertex, or based on what was half weight-painted (auto weight got the top eye-lids and not the bottom, same with some mouth meshes).

After testing the head movement, I noticed the bottom gumline of the teeth doesn't move with the rest of the mouth, despite having the same vertex weights, Same is true with the eyebrows and eyelashes. When moving the neck bone I noticed the problem persisted with the bottom gum line but not the eyebrows or eye lashes. As far as I can tell the weight painting is the same on both bones. 

The goal is obviously for the eyebrows and eyelashes to move as they do in the neck movement image, and the gumline to stay with it's set of teeth. 

I tried separating the meshes and connecting to the head bone (as you would do with hair?), but when the head and neck moved they didn't keep their position on/in the head. Does anyone know how I can fix all this?
If two vertices, even if near to each other, move differently, surely they have different weights.

When using automatic weighting, this common problem arise when some vertices get weight from some bones and other form more (or less) bones, so if you check only the head and the neck they seem similar, but in fact they are different.

In edit mode, if you select a group of vertices you can read the weights of the active one (last selected) in the N properties panel, so making a comparision between two vertices that have a different behaviour will underline where the problem lies.

An useful trick is to use the "selected to active" function, in which you select a group of vertices (like all bottom teeth), then shift select the vertex to follow (in my example it could be the center vertex), and press the little folder button (you have to do it for all the involved vertex groups, if some vertex group have influence on the selected vertices but not on the active, you have to use the remove button in the vertex weight tab).