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Gravity is equivalent to acceleration. So it would be as if the light clock in the example was moving faster and faster, changing from one reference frame to another one. And as it moved faster and faster, three things would happen (according to Special Relativity Theory):

1) The moving object progressively shrinks in length (from the outside stationary observer's point of view)

2) Time aboard the moving frame progressively slows (from the outside stationary observer's point of view)

3) The mass of the clock, and any other mass-containing object aboard the moving frame, progressively increases (from the outside stationary observer's point of view)

Certainly mass effects the fabric of space, but these effects wouldn't come into play here with such low mass objects. There isn't anywhere near the amount of mass here to bend the light beam's path. To bend a light beam's path, you need extreme amounts of mass, somewhere around the mass of the Sun. In fact, it was the bending of light coming from planet Mercury around the Sun which helped confirmed Einstein's GENERAL Theory of Relativity. Special Relativity only applies to things moving at a constant velocity (straight line, constant speed, basic inertial motion), while General covers it all.

1st of all, thanks for indulging me, I don't get very many opportunities to talk about this stuff.

On first glance, I didn't realize that ALL of the components within the light clock diagram were contained within the inertial frame, and I jumped to conclusion based upon that.

[three things would happen (according to Special Relativity Theory)]

It seems the interpretation of these observations is dependent upon one's understanding of the nature of time itself.

If time doesn't exist independently from the system - independent of the inertial frame being observed - then we're left having to explain any observed dilation/constriction of time as being an effect of the progressive relationship between Energy, Mass, and Space within that inertial frame.

The observation is that time progresses relative to the speed of the inertial frame.

If time is derived solely from state changes within an inertial frame; then what is happening within the inertial frame that accounts for the inverse relationship between speed and time? If I now understand the light-clock model correctly, the answer is thus:

If the state change being measured is the movement of a beam of light between two points, and C is constant, then, in order for "time" to slow down, the distance between the two points within the inertial frame must be increasing. Is that correct?

But this would seem to contradict the idea that 1) The moving object progressively shrinks in length

It seemingly creates a paradox where, simultaneously, as the volume of the observed inertial frame appears to become smaller (from the outside stationary observer's point of view), it must also be expanding within, in order to account for the slowing progression of state change (time) as derived from C.

How is that resolved?

More "space" is compressed into the inertial frame?

[Certainly mass effects the fabric of space, but these effects wouldn't come into play here with such low mass objects. There isn't anywhere near the amount of mass here to bend the light beam's path.]

But as the velocity of a body increases, its mass increases and approaches infinity as V approaches C.

Wouldn't mass become sufficient to bend light as V approached C?