The experimental manifestation of topological effects in bulk materials is attracting enormous research interest. However, direct experimental evidence of the effective k-space monopole of the Weyl nodes has so far been lacking. Here, signatures of the singular topology of the type-II Weyl semimetal TaIrTe4 are revealed in the photoresponses, which are related to divergence of the Berry curvature. TaIrTe4 exhibits a large photoresponsivity of 130.2 mA W-1-with 4 mu m excitation in an unbiased field-effect transistor at room temperature-arising from the third-order nonlinear optical response, approaching the performance of commercial low-temperature detectors. In addition, the circularly polarized galvanic response is enhanced at 4 mu m, possibly due to the same Berry curvature singularity enhancement. Considering the optical selection rule of chiral Weyl cones, this may open the door for studying and controlling the chiral polarization of Weyl fermions with an electric field in addition to the optical helicities.