This paper proposes a novel multi-agent deep reinforcement learning (MADRL)-based positioning algorithm for multiple unmanned aerial vehicles (UAVs) collaboration in mobile access applications where the UAVs work as mobile base stations. The primary objective of the proposed algorithm is to establish reliable mobile access networks for vehicle-to-everything (V2X) communications. This paper jointly considers energy-efficient UAV operation and reliable wireless communication services for realizing robust mobile access services. For the energy-efficient UAV operation, the reward function formulation of our proposed MADRL algorithm contains the features for UAV energy consumption models in order to realize efficient operations. Furthermore, for the reliable wireless communication services, the quality of service (QoS) requirements of individual users are considered as a part of reward function. Furthermore, this paper considers 60 GHz millimeter-wave (mmWave) mobile access for utilizing the benefits of i) ultra-wide-bandwidth for multi-Gbps high-speed communications and ii) high-directional communications for spatial reuse that is obviously good for avoiding interference among densely deployed users. Lastly, the comprehensive and data-intensive performance evaluation of the proposed MADRL-based algorithm for multi-UAV positioning is conducted. The results of these evaluations demonstrate that the proposed algorithm outperforms other existing algorithms.