The non-Hermitian skin effect (NHSE), characterized by extensive boundary accumulation of eigenstates under open boundary conditions, has emerged as a central phenomenon in non-Hermitian physics. Established routes to the NHSE are usually based on Abelian nonreciprocal mechanisms, including an equivalent approach involving gain and loss combined with synthetic gauge fields. Here, we demonstrate that non-Abelian couplings can generate the NHSE through a distinct reciprocal mechanism, giving rise to a time-reversal-symmetry-protected $Z_2$ skin effect with pseudospin-resolved boundary localization and dynamical pseudospin separation. We further show that local breaking of time-reversal symmetry at a boundary induces a pseudospin-inversion reflection process, converting the bidirectional $Z_2$ skin response into unidirectional boundary localization. Experimentally, we implement a representative four-level model using a programmable topolectrical circuit and directly observe both the predicted NHSE and the boundary-induced pseudospin-inversion reflection. Our results identify non-Abelian coupling as a mechanism for symmetry-controlled skin effects in reciprocal systems, opening new avenues for realizing nonreciprocity-free topological materials and devices.

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• Symmetry protected topological states
• Non-Hermitian systems
• Topology