We report Te-doped GaP nanowires (NWs) with positive tapering and radii measuring as low as 5 nm grown by the self-assisted vapor-liquid-solid mechanism using selective-area molecular beam epitaxy. The occurrence of the ultrathin nanoantenna showed a dependence on pattern pitch (separation between NWs) with a predominance at 600 nm pitch, and exhibited radius oscillations that correlate with polytypic zincblende/wurtzite segments. A growth model explains the positive tapering of the NW leading to an ultrathin tip from the suppression of surface diffusion of Ga adatoms on the NW sidewalls by Te dopant flux. The model also provides a relationship between the radius modulations and the oscillations of the droplet contact angle, predicting the quasi-periodic radius oscillations and corresponding crystal phase transitions. The GaP NWs showed strong low temperature micro-photoluminescence exciton-related emission, indicating a bandgap difference between the zincblende/wurtzite segments, with phonon replicas due to the transverse optical phonon mode. These results establish a link between dopants and the ability to control NW morphology, crystal phase and luminescent properties with possible applications in thermoelectrics, quantum emitters and photodetectors.