Once thought to be devoid of warm and cold interstellar matter, elliptical galaxies are now commonly observed to host extended regions of neutral and ionized gas. Outside of the innermost nuclear regions of these galaxies, the favoured candidate ionizing source remains some component of the stellar population, with mounting evidence suggesting post-asymptotic-giant-branch stars (pAGBs). In a recent paper, we demonstrated that observations of recombination lines of He ii (or upper limits thereof) may provide a strong constraint on the presence of any other, higher temperature ionizing sources, in particular nuclear-burning white dwarfs (WDs) in the context of the single-degenerate (SD) scenario for Type Ia supernovae. The sensitivity of the He ii test is greatest for WD effective temperatures ∼2 × 105 K. Here, we extend our analysis to include predictions for all of the ‘classical’ strong optical lines, as well as UV, optical and infrared lines of neutral oxygen, nitrogen and singly ionized carbon. This allows us to extend the temperature range over which we can meaningfully constrain the collective luminosity of nuclear-burning WDs to 105 K ≲ T ≲ 106 K. We then demonstrate how observations of nearby early-type and post-starburst galaxies can place strong limits on the origin of Type Ia supernovae.