The versatility and large work envelope have made robots a fixture in the field of assembly for years. However, their lower stiffness and pose dependency require robust models to find optimal trajectories even for high accuracy applications. A significant obstacle in this domain is parametrizing such models of compliant robots during operation. Addressing this gap, and considering the trend of robots performing manufacturing tasks in parallel with assembly, we present an automated identification process to estimate the stiffness and damping parameters of robot joints within a milling process. This method relies solely on universally accessible kinematic chain data and force and acceleration measurements at the tool center point, eliminating the need for specialized equipment. The approach is based on a multi-body simulation, which includes flexible 6-DOF bushing joints. Key to our approach is using Jacobian-based sensitivities inside a Random Search (RS) algorithm to navigate the complexities of a sparse multi-dimensional parameter space. Our approach is versatile enough to accommodate various parameter types. We test our approach on a simulated 3-joint robot with 6 DOF per joint. By pairing the Jacobian-based sensitivities with adaptions made to the RS algorithm, we obtain accurate predictions for unknown input data with a mean relative displacement error of 2%.