Can a tertiary enamine tautomerize to an imine?
Tautomerization is a chemical reaction whereby constitutional isomers interconvert. The interconversion process involves the shift of a hydrogen atom accompanied by the shift of a double bond.  Here are a few examples.



In molecule (a) pictured above, there is no hydrogen attached to a nitrogen (it has been replaced by a methyl group), so there is no hydrogen atom available to shift.

Response to OP's edit:

The picture you posted in your edit is incorrectly labeled.  The charged molecule on the left is an iminium ion, not an imine.  So this is not an example of an imine-eneamine equilibrium.  You are correct that in this equilibrium (the one pictured in your edit) there is no hydrogen transferred to nitrogen, but again, this is not an example of an imine-eneamine tautomerization.  I think this error is the source of your confusion.

Here is a picture of an imine-eneamine tautomerization.

 

As you can see, a hydrogen is transferred between nitrogen and carbon.  This hydrogen transfer can occur with or without solvent molecules playing a role.  That is to say, the hydrogen can be transferred directly between the carbon and nitrogen atoms, or it can be transferred from one of the atoms to a solvent molecule which can then transfer it back to the other atom involved in the tautomerization. The image source also provides a nice explanation of tautomerization.