Let $k$ be a field with algebraic closure $\bar{k}$.

Recall that a gerbe over $k$ is an algebraic stack $\mathcal{G}$ over $k$ such that the groupoid $\mathcal{G}(\bar{k})$ is connected. We say that $\mathcal{G}$ is neutral if $\mathcal{G}(k)$ is non-empty.

Now assume that $k = \mathbb{F}_q$ is a finite field.

Is any gerbe over $\mathbb{F}_q$ neutral?

Gerbes are classified by 2nd Galois cohomology, and $\mathbb{F}_q$ has cohomological dimension $1$ which is why I suspect this is the case. But there are a lot of subtleties to the theory, e.g. abelian vs non-abelian gerbes or banded vs non-banded gerbes. So there could be some technicalities I'm over looking (perhaps even my take on the definition of a gerbe is too naive?)