Image-based feature representation plays a critical role in visual localization, enabling robots to estimate their position and orientation in GPS-denied environments. However, this task is often undermined by significant variations in camera viewpoints and scene appearances. Recently, map-free visual relocalization (MFVR) has emerged as a promising paradigm due to its compatibility with lightweight deployment and privacy isolation on mobile devices. In this paper, we propose the Debiased Multiplex Tokenizer (DeMT) as a novel method for versatile and efficient MFVR. Specifically, DeMT performs relative pose regression through an integrated framework built upon a pretrained vision Mamba encoder, comprising three key modules: First, Multiplex Interactive Tokenization yields robust image tokens with non-local affinities and cross-domain descriptions; Second, Debiased Anchor Registration facilitates anchor token matching through proximity graph retrieval and causal pointer debiasing; Third, Orthogonal Pose Regression enhances both pair-wise and multi-view pose regression via Jacobi polynomial parsing of Kolmogorov–Arnold networks. Extensive evaluations across ten public datasets demonstrate that DeMT substantially outperforms existing benchmarks and ablation variants in diverse indoor and outdoor environments. Our code and models will be released upon paper acceptance.