This work addresses critical gaps in the Multi-connection Tactile Internet Protocol (MTIP) by introducing three key enhancements for secure and energy-efficient Tactile Internet systems: (1) lightweight mutual authentication using pre-shared keys, (2) timestamp-bound XOR encryption for confidentiality, and (3) adaptive sleep modes reducing energy consumption by 47-65%. Using UPPAAL, we formally modeled the proposed enhanced MTIP and formally analyzed/verified its correctness, proving security properties (authentication integrity, data confidentiality, tamper detection) and preserving sub-millisecond latency guarantees. The enhanced MTIP maintains reliability through multi-path redundancy even during sleep transitions, ensuring robustness in safety-critical applications like remote surgery and industrial automation. By integrating formal verification with practical optimizations, this work transforms MTIP into a deployable solution for next-generation haptic networks, balancing security, energy efficiency, and real-time performance.