Spinor Euler factors for GSp(4) in the subregular case

For local non-archimedean fields $k$, Piatetski-Shapiro has defined local spinor $L$-factors for irreducible representations $\Pi$ of $\mathrm{GSp}(4,k)$ of dimension $>1$, attached to a choice of a Bessel model $\Lambda$. We classify regular poles that do not come from the asymptotic of the Bessel functions in the Bessel model. For anisotropic Bessel models there are no such subregular poles.