We propose schemes for the detection of topological defect dark matter using pulsars and other luminous extraterrestrial systems via nongravitational signatures. The dark matter field, which makes up a defect, may interact with standard model particles, including quarks and the photon, resulting in the alteration of their masses. When a topological defect passes through a pulsar, its mass, radius, and internal structure may be altered, resulting in a pulsar "quake." A topological defect may also function as a cosmic dielectric material with a distinctive frequency-dependent index of refraction, which would give rise to the time delay of a periodic extraterrestrial light or radio signal, and the dispersion of a light or radio source in a manner distinct to a gravitational lens. A topological defect passing through Earth may alter Earth's period of rotation and give rise to temporary nonzero electric dipole moments for an electron, proton, neutron, nuclei and atoms.