The design of efficient graphene-silicon (GSi) Schottky junction photodetectors requires detailed understanding of the spatial origin of the photoresponse. Scanning-photocurrent-microscopy (SPM) studies have been carried out in the visible wavelengths regions only, in which the response due to silicon is dominant. Here we present comparative SPM studies in the visible ($\lambda$ = 633nm) and infrared ($\lambda$ = 1550nm) wavelength regions for a number of GSi Schottky junction photodetector architectures, revealing the photoresponse mechanisms for silicon and graphene dominated responses, respectively, and demonstrating the influence of electrostatics on the device performance. Local electric field enhancement at the graphene edges leads to a more than ten-fold increased photoresponse compared to the bulk of the graphene-silicon junction. Intentional design and patterning of such graphene edges is demonstrated as an efficient strategy to increase the overall photoresponse of the devices. Complementary simulations and modeling illuminate observed effects and highlight the importance of considering graphene's shape and pattern and device geometry in the device design.