Have a look at this site.
http://www.puppetsandprops.com/TheFredProject.html It will give you an idea of how things work inside a vent dolls head. Now he has used springs to keep the mouth closed. Pulling on the string opens the mouth. You can use springs with cable control also if you want or you can leave them with out.
Click on the "Installing Mechanics". See the wheel in the base of the head that the string is running over? I would say that is about the location you would mount the sleeve of your cable. Remember you want to leave enough room from the end of the sleeve to where it attaches so that you get the full pull action you need. How would you test that? It needs to be a bit beyond where the connect to the lower jaw would be if open.
Here Goggle "Google Search:
puppet mechanism" then look at the image results for the search. You'll find a ton of images of puppet innards. Might give you some more ideas. BTW there is never just one way to do something. Don't be afraid to experiment.