We study a non-Markovian two-qubit collision model through its Markovianfour-atom embedding and argue that, in this setting, defectivity is most naturally formulatedat the level of the embedded GKSL Liouvillian. In the relevant invariant sector thegenerator separates into explicit relaxation and coherence blocks that contain both defectivecoherence channels and a Jordan-3 relaxation subchannel. After projection onto the stablesubspace, the associated Lyapunov equation remains well posed for positive probes andyields finite but strongly anisotropic diagnostics; numerical benchmarks on documentednear-critical paths then show that unconstrained optimization is coherence dominated,whereas a balanced objective selects a compact mixed probe. A Hermitian surrogate retainsmost of this optimized response and supports experimentally readable finite-windowdrive/readout protocols, so the paper offers a controlled, model-specific route from embeddedJordan geometry to probe design and readout construction rather than a generaltheory of non-Markovian exceptional points.