Reliable identification of nonlinear dynamics remains challenging when the governing mechanical effects are only partially known and measurement data contains substantial temporal gaps. These situations often occur in multibody systems when sensor dropouts or harsh operating conditions degrade the data quality. In such scenarios, classical white-box models struggle because incomplete physical knowledge leads to imprecise predictions, and stiff ordinary differential equations entail excessive computation times. Pure black-box approaches, in contrast, require coherent training data and thus fail when confronted with extended data-gaps. To compensate these insufficiencies, a gray-box modeling strategy in form of a Physics-Informed Neural Network (PINN) is proposed, which blends partially known physics with data-driven model performance. This work investigates the less-studied problem of how PINNs can compensate substantial temporal data gaps while maintaining fast and precise predictions by embedding only partially known mechanics directly into the learning process. A nonlinear, viscously damped four-bar linkage operating in honey fluid is studied, for which state-dependent damping mechanisms cannot be modeled sufficiently. A PINN is trained using real-world measurement data, enforcing Lagrangian-based constraints of the known mechanics while allowing data-driven learning of unmodeled effects. As a baseline, a white-box state-space model (SSM) is identified using Lagrangian mechanics combined with particle swarm optimization for parameter identification to ensure fair comparison. Furthermore, the trade-off between computation time and discretization requirements is investigated. The PINN achieves a ∼37% lower mean-squared error compared to the parameter-optimized SSM and provides 13-times faster inference due to its mesh-free formulation. It further facilitates long-term stable predictions across both states, even under substantial training-data gaps. The findings highlight that PINNs are able to simultaneously reconcile partially known dynamics with substantial data gaps, and thus provide a robust modeling framework for dynamical systems.