Gate-tunable Josephson junctions are interesting for quantum technology applications, such as gatemon qubits and topological Majorana-based qubits. Furthermore, high-frequency compatible geometries can be utilized for implementing electrically pumped parametric amplifiers. In this paper, we combine processing, measurements, and modeling of near-surface InGaAs Josephson field-effect transistors in order to facilitate circuit simulations of actual non-ideal devices. We developed a compact model using Verilog-A and confirmed the validity of our model by accurately reproducing our measured data by circuit simulations in Advanced Design System. From the circuit simulations, an effective gate-dependent transmission coefficient, with a peak value of ∼ 3.5%, was extracted, mainly limited by contact transparency.