We report new multi-colour photometry and high-resolution spectroscopic observations of the long-period variable V501 Aur, previously considered to be a weak-lined T-Tauri star belonging to the Taurus-Auriga star-forming region. The spectroscopic observations reveal that V501 Aur is a single-lined spectroscopic binary system with a 68.8-day orbital period, a slightly eccentric orbit (e ~ 0.03), and a systemic velocity discrepant from the mean of Taurus-Auriga. The photometry shows quasi-periodic variations on a different, ~55-day timescale that we attribute to rotational modulation by spots. No eclipses are seen. The visible object is a rapidly rotating (vsini ~ 25 km/s) early K star, which along with the rotation period implies it must be large (R > 26.3 Rsun), as suggested also by spectroscopic estimates indicating a low surface gravity. The parallax from the Gaia mission and other independent estimates imply a distance much greater than the Taurus-Auriga region, consistent with the giant interpretation. Taken together, this evidence together with a re-evaluation of the LiI~$lambda$6707 and H$alpha$ lines shows that V501 Aur is not a T-Tauri star, but is instead a field binary with a giant primary far behind the Taurus-Auriga star-forming region. The large mass function from the spectroscopic orbit and a comparison with stellar evolution models suggest the secondary may be an early-type main-sequence star.
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