Reconfigurable antennas (RAs) utilize the electromagnetic (EM) domain to provide dynamic control over antenna radiation patterns, which offers an effective way to enhance power efficiency in wireless links. Unlike conventional arrays with fixed element patterns, RAs enable on-demand beam-pattern synthesis by directly controlling each antenna's EM characteristics. While existing research on RAs has primarily focused on improving spectral efficiency, this paper explores their application for downlink localization. Moreover, the majority of existing works focus on far-field scenarios with little attention on near-field (NF). Motivated by these gaps, we consider a synthesis model in which each antenna generates desired beampatterns from a finite set of EM basis functions. We then formulate a joint optimization problem for the baseband (BB) and EM precoders with the objective of minimizing the user equipment (UE) position error bound (PEB) in NF conditions. Our analytical derivations and extensive simulation results demonstrate that the proposed hybrid precoder design for RAs significantly improves UE positioning accuracy compared to traditional non-reconfigurable arrays.