I can tell you, that a low level came also during engine run on my MK I.
Confirmed.
MK1 and MK2 had purely analogue technique here. These level sensors were always "hot" with ignition switched on. They were directly wired to the display unit (auxiliary driver information module). This unit only made the time delay against erratic signals and then triggered the signalling bulb. That's it.
With the MK4 and above, the level switch is another input signal to the digital processor inside the BCM. All is software here. It needs to be tested if the mentioned input pin is already supportet by the software or not.