On the Brauer group of a generic Godeaux surface

Let $X$ be a Godeaux surface over $\mathbb{C}$ and $q_X\text{\hspace{0.17em}⁣}:Y\to X$ be its universal cover. We show that the pullback map $q_X^{\ast }\text{\hspace{0.17em}⁣}:Br(X)\to Br(Y)$ is injective if $\rho (Y)=9$. Our arguments rely on a degeneration technique that also applies to other examples.