This paper proposes a non-uniform beam pattern modulation (NUBPM) scheme for integrated sensing and communication (ISAC) systems, where the beam pattern indices are adopted to carry additional information, increasing the spectral efficiency. We analyze the sensing performance and spectral efficiency of the proposed NUBPM scheme, which depends on the beam patterns and their activation probabilities. Furthermore, to improve the performance of the NUBPM-enabled ISAC systems, we investigate the beam pattern set design and activation probability optimization. Simulation results show that the proposed scheme considerably outperforms existing ISAC designs in spectral efficiency while keeping the same sensing performance. The gained spectral efficiency through the proposed scheme can also be traded off for novel equilibria between communication and sensing performance for ISAC systems.