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The preprint "Conjecture de type de Serre et formes compagnons pour $GSp_4$" by Florian Herzig and Tilouine (available here) indicates that there should be two 1's and two -1's.
EDIT: Having come in to work today, I could look up the more precise statement given in chapter 9 of Tilouine's book "Deformations of Galois representations and Hecke algebras" (incorrectly referenced in the aformentioned article of Herzig–Tilouine). The statement is the following: Let $G=GSp(4)$, let $\pi$ be a regular algebraic cuspidal automorphic representation of $G(\mathbf{A}_F)$, where $\mathbf{A}_F$ is the adele ring of a number field $F$. Let $\bar{\rho}$ be the associated mod $p$ Galois representation. Let $v$ be a real place of $F$. Then the $G$-conjugacy class of ${\bar\rho}(c_v)$ (where $c_v$ is a complex conjugation at $v$) contains the matrix $\text{diag}(1,1,-1,-1)$.
The preprint "Conjecture de type de Serre et formes compagnons pour $GSp_4$" by Florian Herzig and Tilouine (available here) indicates that there should be two 1's and two -1's.