The generalization of the Dirac equation to the cases of other than spin 1/2 is the Duffin–Kemmer-Petiau Equation. Strictly speaking, this applies to systems with non-zero rest-mass $m$, but it can be directly adapted - as is - by setting $m = 0$, to handle light-speed particles, just as it can for the Dirac equation. I don't believe there will be any complications or road-blocks in doing so.
It might be possible to mash it up with Peter Mohr's Solutions Of The Maxwell Equations And Photon Wave Functions (National Institute Of Standards And Technology) - but to handle gauge-fixing, it will require adding in an 11th component, instead of the 10 that normally go with the Kemmer equation for mass non-zero spin 1. The starting point is Mohr's
$$∇·𝐄 = \frac{ρ}{ε_0},\label{1}\tag{1}$$
$$∇×𝐁 - \frac{1}{c^2}\frac{∂𝐄}{∂t} = μ_0𝐉,\label{2}\tag{2}$$
$$∇×𝐄 + \frac{∂𝐁}{∂t} = 𝟬,\label{3}\tag{3}$$
$$∇·𝐁 = 0,\label{4}\tag{4}$$
where $c = 1/\sqrt{ε_0μ_0}$.
Delve deeper into the potentials to replace ($\ref{3}$) and ($\ref{4}$) by
$$-∇φ - \frac{∂𝐀}{∂t} = 𝐄,\tag{3A}$$
$$∇×𝐀 = 𝐁.\tag{4A}$$
Write down an extra equation for the Lorenz term
$$∇·𝐀 + \frac{1}{c^2}\frac{∂φ}{∂t} = b.\tag{0A}\label{0A}$$
Modify ($\ref{1}$) and ($\ref{2}$) by off-setting the Lorenz term
$$∇·𝐄 + \frac{∂b}{∂t} = \frac{ρ}{ε_0},\tag{1A}\label{1A}$$
$$∇×𝐁 - \frac{1}{c^2}\frac{∂𝐄}{∂t} - ∇b = μ_0𝐉.\tag{2A}\label{2A}$$
Then, try to apply the remainder of Mohr's paper to these equations, instead. The matrix representation is $11×11$, instead of the usual $10×10$ representation for the massive spin 1 case.
It's still possible to add in a mass term, and make the equations Proca equations. This requires further modification of ($\ref{1A}$) and ($\ref{2A}$) to
$$∇·𝐄 + \frac{∂b}{∂t} = \frac{ρ}{ε_0} - \frac{φ}{λ^2},\tag{1B}\label{1B}$$
$$∇×𝐁 - \frac{1}{c^2}\frac{∂𝐄}{∂t} - ∇b = μ_0𝐉 - \frac{𝐀}{λ^2},\tag{2B}\label{2B}$$
corresponding to a boson of mass $m = ħ/(λc) > 0$. In both cases, the gauge needs to be fixed by applying the Lorenz condition $b = 0$, or whatever refinement to it is required for quantization. For the case $m > 0$, ($\ref{0A}$) can be removed, and $b$ can be removed from ($\ref{1B}$) and ($\ref{2B}$), because $b = 0$ will already follow as a consquence. The inclusion of $b$ is to make it easier to handle the $m = 0$ case.