With the rapid growth of interconnected devices in Industrial and Medical Internet of Things (IIoT and MIoT) ecosystems, ensuring timely and accurate detection of cyber threats has become a critical challenge. This study presents an advanced intrusion detection framework based on a hybrid Squeeze-and-Excitation Attention Vision Transformer-Bidirectional Long Short-Term Memory (SE ViT-BiLSTM) architecture. In this design, the traditional multi-head attention mechanism of the Vision Transformer is replaced with Squeeze-and-Excitation attention, and integrated with BiLSTM layers to enhance detection accuracy and computational efficiency. The proposed model was trained and evaluated on two real-world benchmark datasets; EdgeIIoT and CICIoMT2024; both before and after data balancing using the Synthetic Minority Over-sampling Technique (SMOTE) and RandomOverSampler. Experimental results demonstrate that the SE ViT-BiLSTM model outperforms existing approaches across multiple metrics. Before balancing, the model achieved accuracies of 99.11% (FPR: 0.0013%, latency: 0.00032 sec/inst) on EdgeIIoT and 96.10% (FPR: 0.0036%, latency: 0.00053 sec/inst) on CICIoMT2024. After balancing, performance further improved, reaching 99.33% accuracy with 0.00035 sec/inst latency on EdgeIIoT and 98.16% accuracy with 0.00014 sec/inst latency on CICIoMT2024.