We present GazeOnce360, a novel end-to-end model for multi-person gaze estimation from a single tabletop-mounted upward-facing fisheye camera. Unlike conventional approaches that rely on forward-facing cameras in constrained viewpoints, we address the underexplored setting of estimating the 3D gaze direction of multiple people distributed across a 360° scene from an upward fisheye perspective. To support research in this setting, we introduce MPSGaze360, a large-scale synthetic dataset rendered using Unreal Engine, featuring diverse multi-person configurations with accurate 3D gaze and eye landmark annotations. Our model tackles the severe distortion and perspective variation inherent in fisheye imagery by incorporating rotational convolutions and eye landmark supervision. To better capture fine-grained eye features crucial for gaze estimation, we propose a dual-resolution architecture that fuses global low-resolution context with high-resolution local eye regions. Experimental results demonstrate the effectiveness of each component in our model. This work highlights the feasibility and potential of fisheye-based 360° gaze estimation in practical multi-person scenarios. Project page: https://caizhuojiang.github.io/GazeOnce360/.