Procedural eyes + armature = bloody-red mess
The eyes are built procedurally. The shader makes heavy use of the object coordinates and is a bit prone to changes in the object's origin and scale.
You have parented the eyes to the armature. This applies an Armature modifier which deforms the mesh. The eyeballs don't get deformed but moved down when you play the sit-down animation. The origin (orange dot) stays where it is during the animation, just the mesh is moved. This finally messes up the procedural shader of the eyes. The iris disappears and the bloody back of the eye with all the veins begins to cover the entire eyeball.
How to fix Rigify eyes
In a nutshell: remove the Armature modifier from the eyeball objects and parent them to the bones
MCH-eye.L of the generated rig (not the metarig).
Make sure the origin of the eyeball is at the center and the bones of the metarig are at the center of the eyeballs else the eyes will stick out of the head when they are rotated. You can use the 3D Curser (Shift+S pie menu) to align them.
If the bones are a bit off re-generate the rig to have all relevant bones in the right place. Remember to make a backup copy of the mesh with the weight paint if you did already some weight paint. Then align the bones with the eyeballs, and re-generate the rig from the metarig.
Parent the eyeballs to the bones
MCH-eye.L of the rig. The MCH- bones are on layer 31. In Object mode, select the first eyeball, then select the rig additionally (eyeball is selected red, rig is selected in orange). Switch to Pose mode, select the bone, and parent the eyeball to the bone (Ctrl+P, Parent to ... Bone).
Once you have (re-)generated the rig and parented the armature to the mesh you need to weight paint the eyelids (or transfer the weights from a backup copy if you already did this step). See Why are my model's eyes deforming so badly? for details.
Hope this helps ...
I can see you ;-)