Mobile target search is a problem pertinent to a variety of applications, including wilderness search and rescue. This paper proposes a hybrid approach for target search utilizing a team of mobile agents supported by a network of static sensors. The approach is novel in that the mobile agents deploy the sensors at optimized times and locations while they themselves travel along their respective optimized search trajectories. In the proposed approach, mobile-agent trajectories are first planned to maximize the likelihood of target detection. The deployment of the static-sensor network is subsequently planned. Namely, deployment locations and times are optimized while being constrained by the already planned mobile-agent trajectories. The latter optimization problem, as formulated and solved herein, aims to minimize an overall network-deployment error. This overall error comprises three main components, each quantifying a deviation from one of three main objectives the network aims to achieve: (i) maintaining directional unbiasedness in target-motion consideration, (ii) maintaining unbiasedness in temporal search-effort distribution, and, (iii) maximizing the likelihood of target detection. We solve this unique optimization problem using an iterative heuristic-based algorithm with random starts. The proposed hybrid search strategy was validated through the extensive simulations presented in this paper. Furthermore, its performance was evaluated with respect to an alternative hybrid search strategy, where it either outperformed or performed comparably depending on the search resources available.