Integer-valued rational functions over globalized pseudovaluation domains

$\text{DeclareMathOperator}\text{IntR}Int{}^{\text{R}}$$\text{DeclareMathOperator}\text{Int}Int$Let $D$ be a domain. Park determined the necessary and sufficient conditions for which the ring of integer-valued polynomials $\text{Int}(D)$ is a globalized pseudovaluation domain (GPVD). In this work, we investigate the ring of integer-valued rational functions $\text{IntR}(D)$. Since it is necessary that $D$ be a GPVD for $\text{IntR}(D)$ to be a GPVD, we consider $\text{IntR}(D)$, where $D$ is a GPVD. We determine that if $D$ is a pseudosingular GPVD, then $\text{IntR}(D)$ is a GPVD. We also completely characterize when $\text{IntR}(D)$ is a GPVD if $D$ is a pseudovaluation domain that is not a valuation domain.