The impedance of the battery varies according to the strength of the electrolyte and electrolyte level. If your battery has a low or dry (!) cell, your battery becomes a rather poor, leaky capacitor. There are various inductors in the charge circuit, and they create a pretty efficient LC filter. If your battery is dying, it changes capacitance and the characteristics of the "filter", so any ripple on the AC lines goes straight out on your 12V DC feed lines, switched or permanent.

One of the few remaining Mk1 owners... #00015