In so many classes I’ve been told that light is nothing more than an electromagnetic wave. While this makes sense, it’s never been nearly as clear as imagining a static charge. At every point in space surrounding the static charge we can assign a vector representing the electric field. What about light? I know maxwells equation for $p=0$ give us something like $E=Acos(kx-wt)$ but I feel there is something not being explicitly stated. It’s not like x can assume any value, correct? I’d assume x would be confined to the photons trajectory. Otherwise what does this equation even give us? It would imply that there’s an electric field present everywhere always. I’ve seen animations of EM waves orthogonal to each other on an axis but I couldn’t imagine that the entire axis has an electric field, and also have trouble thinking about how the waves are shown in two dimensions.

So to quickly state my question, if we took snapshots of a photon and could see the EM wave at all points in space in each, what would we see? Would the field only exist at the singular point the photon resides at, would there be a field surrounding the photon (in the same way the electric field of a static charge does), does the field trail behind the photon as it travel, etc

If I’m not wrong, Maxwells equations and the equation for EM radiation predated quantum theory, so how was this equation interpreted then, with the assumption the particle would always assume a definite position?

In so many classes I’ve been told that light is nothing more than an electromagnetic wave. While this makes sense, it’s never been nearly as clear as imagining a static charge. At every point in space surrounding the static charge we can assign a vector representing the electric field. What about light? I know Maxwell's equations for $\rho=0$ give us something like $E=A\cos(kx-\omega t)$, but I feel there is something not being explicitly stated. It’s not like $x$ can assume any value, correct? I’d assume $x$ would be confined to the photon's trajectory. Otherwise, what does this equation even give us? It would imply that there’s an electric field present everywhere always. I’ve seen animations of electromagnetic waves orthogonal to each other on an axis, but I couldn’t imagine that the entire axis has an electric field, and also have trouble thinking about how the waves are shown in two dimensions.

So to quickly state my question, if we took snapshots of a photon and could see the electromagnetic wave at all points in space in each, what would we see? Would the field only exist at the singular point the photon resides at, would there be a field surrounding the photon (in the same way the electric field of a static charge does)? Does the field trail behind the photon as it travels? Etc.

If I’m not wrong, Maxwell's equations and the equation for electromagnetic radiation predated quantum theory, so how was this equation interpreted then, with the assumption the particle would always assume a definite position?