We use CASSCF and MRPT2 calculations to characterize the bridge photoisomerization pathways of a model red fluorescent protein (RFP) chromophore model. RFPs are homologues of the green fluorescent protein (GFP). The RFP chromophore differs from the GFP chromophore via the addition of an N-acylimine substitution to a common hydroxybenzylidene-imidazolinone (HBI) motif. We examine the substituent effects on the manifold of twisted intramolecular charge-transfer (TICT) states which mediates radiationless decay via bridge isomerization in fluorescent protein chromophore anions. We find that the substitution destabilizes states associated with isomerization about the imidazolinone-bridge bond and stabilizes states associated with phenoxy-bridge bond isomerization. We discuss the results in the context of chromophore conformation and quantum yield trends in the RFP subfamily, as well as recent studies on synthetic models where the acylimine has been replaced with an olefin.