Large Language Models (LLMs) exhibit strong language understanding and instruction-following abilities, making them promising backbones for grammatical error correction (GEC). However, prompt-only correction for low-resource languages still suffers from the over-correction challenge, since LLMs cannot fully understand their internal grammar. To address this issue, we propose an automatic linguistic neuron probing and optimizing approach to improve the low-resource GEC with only a few neuron activations. Concretely, we first utilize multiple low-resource GEC corpora to observe the changes in neurons, thus obtaining a linguistically specific probe matrix to ensure whether the neuron is activated. Then, we construct an extra weight matrix to determine the activation intensity of each neuron. Finally, we combine the probe matrix and the weight matrix to obtain an activation matrix, which is injected into selected model layers during inference to guide the frozen LLM toward more controllable GEC. Experiments on four benchmark datasets show that our approach consistently improves GEC performance, indicating that lightweight sparse activation rescaling is extremely useful for low-resource grammatical knowledge understanding. Detailed analysis demonstrates that our approach can further provide interpretable neuron-level control without large-scale parameter fine-tuning.