Spiking neural networks (SNNs) require sequential computation over long timesteps, introducing substantial memory and energy overheads due to frequent updates of neuron membrane potentials. Previous SNN accelerators address this by employing tick-batch techniques, which process all timesteps within a layer before moving on to the next. However, existing approaches rely on neuron-centric scheduling, limiting their ability to exploit temporal sparsity. In this work, we propose a novel scheduling along with its hardware architecture for Gustavson product (GP)-based SNN acceleration. We introduce a column-parallel tick-batch (CPTB) dataflow that partitions the spike matrix into multiple submatrices and processes each submatrix of a timestep in parallel while maintaining tick-batch semantics. To support this, we present the first GP-based SNN accelerator, named GustavSNN, which avoids accessing the global membrane potential memory by updating neuron states directly in local registers. In addition, we propose a non-zero row vector (NRV) spike format that enables fine-grained skipping of inactive spike rows. As a result, our proposed architecture achieves up to 11.8 times higher energy efficiency (TOPS/W) compared to the naive GP-based accelerator and 1.92 times higher energy efficiency compared to state-of-the-art SNN accelerators.