Let $V$ be a valuation ring with fraction field $K$, let $L=K(\alpha)$ be a finite simple extension, and let $A=V[\alpha]\subseteq W$, where $W$ denotes the integral closure of $A$ in $L$. We study homological defect modules associated to the normalization quotient $W/A$ using ordinary derived functors. For every valuation-compatible ideal $I\subseteq A$, we define derived integral closure defects \[ \operatorname{Tor}_i^A(W/A,A/I), \] which measure the failure of reduction modulo $I$ to preserve exactness of the normalization sequence \[ 0\to A\to W\to W/A\to0. \] We prove that these homological defect modules are supported along the conductor locus and vanish under suitable flatness hypotheses. In the Henselian defectless setting, we do not claim that defectlessness alone forces Tor-vanishing; rather, we record a conditional collapse statement under explicit Tor-independence or flat-reduction hypotheses, in which case the derived defect system becomes concentrated in degree zero. The new content is the systematic valuation-theoretic use of these ordinary Tor groups as normalization-defect invariants: we identify their conductor support, isolate the connecting image as the actual obstruction to exact reduction, and compute their \(\pi\)-primary torsion profiles in DVR-order normalizations. In particular, the first derived defect records conductor thickness and the elementary-divisor structure of the normalization quotient \(W/A\), including non-cyclic examples. In ramified DVR-order examples this thickness may reflect ramified structure, but the Tor computation itself is an invariant of the normalization quotient rather than a ramification invariant. The approach is entirely algebraic and valuation-theoretic, using only classical homological methods and avoiding higher-categorical or spectral machinery.