I downloaded the drawings and data from input-inc.com, and the specifications call for servers that seem like overkill for the application.

The servos are for moving the eye flaps, which are very thin plastic parts.
It calls for 6x HS-85BB for controlling the fine motions of rotating the top and bottom eye flaps as well as HS-5496MH and HS-5645MG for moving the full assembly.

I've attached a few screenshots for reference.

I was planning on using some 9g micro servos for the eye flaps, which will require that I modify some of the parts to accomodate them.

I'm confident that they have enough torque, but I'm worndering if I'll have issues with precision.

If anyone has more knowledge about various servo types that could point me in the right direction, that would be helpful.