Following from this and other discussions at this site, I wanted to lay out my view of why Eternalism logically precludes motion. After some consideration, I believe that the best way to do this and to present the critical differences between the two major opposing temporal ontological theories of Eternalism and Presentism is via a discussion of the differences between Eternalism and the Moving Spotlight Theory.

Firstly, a definition of terms:

THE PASSAGE OF TIME
A-Theory: Time passes; the passage of time is real
B-Theory: Time doesn't pass; the passage of time is not real

'According to The B Theory, time is very much like the dimensions of space. Just as there are no genuine spatial properties (like being north), but, rather, only two-place, spatial relations (like north of), so too, according to the B Theorist, there are no genuine A properties. According to The A Theory, on the other hand, time is very different from the dimensions of space. For even though there are no genuine spatial properties like being north, there are, according to the A Theorist, genuine A properties; and time, unlike space, can truly be said to pass, according to The A Theory.'
https://plato.stanford.edu/entries/time/#PreEteGroUniThe

'The difference between A-theorists and B-theorists is often described as a dispute about temporal passage or 'becoming' and 'progressing'. B-theorists argue that this notion is purely psychological. Many A-theorists argue that in rejecting temporal 'becoming', B-theorists reject time's most vital and distinctive characteristic. It is common (though not universal) to identify A-theorists' views with belief in temporal passage.'
https://en.wikipedia.org/wiki/B-theory_of_time

ONTOLOGY/EXISTENCE
Eternalism: 'objects from both the past and the future exist just as much as present objects.'
Presentism: 'only present objects exist.'

However, there is more to Presentism than what exists at the present moment, since the present moment is dynamic:

'Presentism is the view that only present things exist and what’s present changes'. (My emphasis)

Presentism therefore entails temporal passage, i.e. the A-Theory.

ONTOLOGICAL HYBRIDS:
Growing Block Theory: 'According to the growing block universe theory of time (or the growing block view), the past and present exist while the future does not. [...] By the passage of time more of the world comes into being; therefore, the block universe is said to be growing. The growth of the block is supposed to happen in the present, a very thin slice of spacetime, where more of spacetime is continually coming into being.'

The Growing Block theory combines Eternalism's existence of the past with Presentism's existence of the present and non-existence of the future.

In short, the Growing Block theory is a hybrid of Eternalism in the past + Presentism in the present/future.

Moving Spotlight Theory: 'the Moving Spotlight Theory combines Eternalism — the doctrine that past, present, and future times all exist — with “objective becoming.” The claim that there is objective becoming has two parts. First, facts about which time is present are non-relative. That is, even if in some sense each time is present relative to itself, only one time is absolutely present. That time, and only that time, glows with a special metaphysical status. And second, which instant is absolutely present keeps changing. The NOW moves along the series of times from earlier times to later times.'
(Relativity and the Moving Spotlight - Bradley Skow)

'We are naturally tempted to regard the history of the world as existing eternally in a certain order of events. Along this, and in a fixed direction, we imagine the characteristic presentness as moving, somewhat like the spot of light from a policeman's bull's eye traversing the fronts of the houses in a street. What is illuminated is the present, what has been illuminated is the past, and what has not yet been illuminated is the future.'
(C. D. Broad (1923))

In short, the Moving Spotlight theory is a hybrid of Eternalism + Presentism/A-Theory.

More astute readers might now be asking themselves the following question: If Eternalism already contains all of existence at all times, then what can Presentism possibly add to this ontology? For example, Huw Price appears to reject Presentism on these grounds in this video. The answer is quite obvious. What Presentism/A-Theory adds over and above the ontology of Eternalism is: temporal passage. Without temporal passage and the A-Theory, Eternalism is equivalent to the four-dimensional block universe. In other words, the block universe or four-dimensionalism is Eternalism + the B-Theory, which is the logically natural state of Eternalism, as far as I understand it. That is, Eternalism + the B-Theory is just Eternalism, whereas Eternalism + the A-Theory is the Moving Spotlight theory.

Some members of this site, including @SophistiCat and @Douglas Alan have previously claimed that Eternalism does not preclude motion. In that case, my question is: when does motion occur according to Eternalism? It cannot be at the present moment, because motion or temporal passage at the present moment implies the A-Theory, making it not Eternalism, but the Moving Spotlight theory instead. So, does Eternalist motion occur in the past or the future somehow?