Geometric monodromy of double covers of $\mathbb{P}^n$ branched along hyperplane arrangements

Let $n\ge1$, let $m\ge n+3$ be even, and let $\ell$ be an odd prime. Over an algebraically closed field in which $2\ell$ is invertible, we determine the geometric mod-$\ell$ and integral $\ell$-adic monodromy of double covers of $\mathbb{P}^n$ branched along ordered arrangements of $m$ hyperplanes i