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 \[ 0\to A\to W\to W/A\to0. \] The homological identities used in this construction are classical. In particular, the conductor-support statements follow by localization, the connecting image follows from the long exact Tor sequence, and in the DVR-order setting the identity \[ \Tor_1^A(M,A/(\pi^n))\cong M[\pi^n] \] is the standard calculation from the two-term resolution of \(A/(\pi^n)\). The purpose of the paper is to organize these facts in a common valuation-theoretic normalization framework: the quotient \(W/A\), its conductor support, valuation-compatible reductions, connecting images, and, in finite DVR-order situations, the elementary-divisor profile \[ n\longmapsto \ell_V\!\left(\Tor_1^A(W/A,A/(\pi^n))\right). \] The latter profile records the \(\pi\)-primary elementary-divisor structure of \(W/A\) as a \(V\)-module; it is not asserted to recover the full \(A\)-module structure of \(W/A\). No novelty is claimed for the underlying Tor formula. The approach is entirely algebraic and valuation-theoretic and uses only classical homological methods.