[tephra]

so basically. if you disconnect the brown/white and black wires from the chassis/ecu, and then test them you should find that:

with the gauge OFF =
OMH meter between white and black should show 0ohms or thereabouts (ie some continuity)
OMH meter between white and brown should show not-connected or thereabouts (ie no continuity)

with the gauge ON =
OMH meter between white and black should show not-connected or thereabouts (ie no continuity)
OMH meter between white and brown should show 0 ohms or thereabouts (ie some continuity)

if we can at least establish that baseline then we can move forwards.

^ all assuming you have DFS unlinked, FS0 linked?? and power to the HFS3 ...

Also FYI a reading of '0.L' implies NO continuity, it's not the same thing as 0 ohms...