The Beam Gas Vertex (BGV) instrument is a novel non-invasive beam profile monitor and part of the High Luminosity Upgrade of the Large Hadron Collider (LHC) at CERN. Its aim is to continuously measure emittance and transverse beam profile throughout the whole LHC cycle, which is currently not possible using a single device. The BGV consists of a gas target and a forward tracking detector to reconstruct tracks and vertices resulting from beam-gas interactions. The beam profile is inferred from the spatial distribution of the vertices, making it essential to achieve a very good vertex resolution. Extensive simulation studies are being performed to provide a basis for the design of the future BGV. The goal of the study is to ascertain the requirements for the tracking detector and the gas target within the boundary conditions provided by the feasibility of integrating them into the LHC. This contribution will focus on the simulations of the forward tracking detector. Based on cutting-edge track and vertex reconstruction methods, key parameter scans and their influence on the vertex resolution will be discussed.