Tensor resonances in teleparallel Gauss-Bonnet branes

We construct an analytical thick-brane solution in linear teleparallel Gauss-Bonnet gravity using a first-order formalism generated by a sine-Gordon superpotential. The resulting asymptotically ${\mathrm{A}\mathrm{d}\mathrm{S}}_5$ configurations exhibit brane splitting controlled by the dimensionless parameter $q=4\alpha k^2$. An analytical splitting condition is derived and combined with tensor-stability requirements to identify the physically viable parameter region. We show that the tensor spectrum is free of tachyonic instabilities and supports a normalizable graviton zero mode. The massive sector exhibits odd-parity gravitational resonances whose quasi-localization is significantly enhanced near the stability boundary. Our results establish a direct link between brane splitting, tensor stability, and gravitational resonances in teleparallel Gauss-Bonnet braneworlds.