I have read (and experienced myself) that reading with a guide
(finger, ruler, etc.) is easier on the eyes because the eyes are
"designed" to follow movement, or that our eyes are "naturally
attracted to motion".   Another resources says said that the "sweeping
motion of our hands across the page caught the attention of our eyes,
and helped them move more smoothly across the page."

From one website:

"Using your hand eliminates a host of reading problems and even helps
reduce eye strain. Try this: imagine a large five-inch' diameter
circle on the wall across from you. Trace the outline of the circle
with your eyes and notice their movement. Now hold out your arm in
front of you and point your finger at the circle. Trace it again, this
time with your finger following the outline, and your eyes following
your finger. Notice that the movement is now very smooth and fluid."

What I am looking for is authoritative scholarly, academic, and/or
scientific proof of this.  These references might require some
measurement of eye strain (both qualitative and quantitative is ok)
*showing that it's easier on the eyes to read when using a guide*.

I'm expecting links to websites, news/magazine articles, book
references, journal articles, online PDFs, etc.  Through my
organization, I have access to almost all academic journals, so if you
find the journal but find that it requires special access to get it,
don't worry - I probably already have that access so feel free to send
me the reference(s).