She is testing her hand strength by the 'squeeze my fingers' technique:
"Test the patient’s grip by having the patient hold the examiner’s fingers in their fist tightly and instructing them not to let go while the examiner attempts to remove them. Normally the examiner cannot remove their fingers. This tests the forearm flexors and the intrinsic hand muscles. Compare the hands for strength asymmetry."
It's done to test muscle strength of the hand, you compare to the other side. Done with people post stroke to compare, to tests muscle strength with people with MS and to do a comparison test frequently to see if the person is having a transient ischemic attack, a 'pre-stroke'.
I also think the doctor is testing her for Nystagmus. In my opinion she's in the midst of saying , "Look at my nose, don't move your head, and now look over here." If the eyes have rapid oscillation to and fro movements when she does that, it's a sign she has nystagmus. She was testing in the here and now, and probably doing a comparison from it being done many times before. A common sign with post head trauma and Multiple Sclerosis.
"Acquired nystagmus can be caused by a disease (multiple sclerosis, brain tumor, diabetic neuropathy), an accident (head injury), or a neurological problem (side effect of a medication). Hyperventilation, a flashing light in front of one eye, nicotine and even vibrations have been known to cause nystagmus in rare cases."
I've often wondered if Hillary has multiple sclerosis. "Vision problems are often the first symptom of multiple sclerosis, indicating issues within the optic nerve. More than 80 percent of multiple sclerosis (MS) patients will experience eye complications related to the condition – an autoimmune disease that targets the brain and central nervous system. Complications include nystagmus, diplopia (double vision), internuclear ophthalmoplegia and optic neuritis."
In summary, I think the doctor was testing to see if she was having a Transient Ischemic Attack, often a precursor to a stroke. With her history of three blood clots, a concussion, deep vein thrombosis, head trauma and the fact they are going to great lengths to shield her from outside medical evaluation, it make one wonder just how serious her conditions are.
Look at the video in 75
That is where that still is from
She is Not squeezing her fingers
There is no bright light requiring sunglasses. Look at the line-up in the video - no one else is wearing shades. The physician has her sunglasses on the top of her head.