After its discovery in 2016, the white dwarf binary AR Scorpii (AR Sco) remained for several years the only white dwarf system to show pulsed radio emission associated with a fast-spinning white dwarf. The evolutionary origin and the emission mechanism for AR Sco are not completely understood, with different models proposed. Testing and improving these models requires observational input. Here, we report the results of a targeted search for other binary white dwarf pulsars like AR Sco. Using data from Gaia and the Wide-field Infrared Survey Explorer (WISE), we identified 56 candidate systems with similar properties to AR Sco, of which 26 were previously uncharacterized. These were subject to spectroscopic and photometric follow-up observations. Aside from one new binary white dwarf pulsar found, J191213.72‑441045.1, which was reported in a separate work, we find no other systems whose characteristics are akin to AR Sco. The newly characterized systems are primarily young stellar objects (with 10 found) or cataclysmic variables (7 identifications), with the remaining being either blended or non-variable on short time-scales.