It makes no difference, although this does mean your HFS won't work!

Although it doesn't want to be a live feed you want a suitable bulb placed in the line (This could be what is what is damaging them)

On the OE setup the live comes from the instrument cluster, and then you will have a blue wire on the connector which is the same wire you see at the back of the unit.

The wire is well known for breaking, due to the heat from the turbo, so I suspect you have a break in this wire and the live is fine.

In which case just rewire this part, with a small ring connector to connect to the alternator.

FYI, the 'W' terminal is not used, this is for Tachos on Diesels mainly, and electronic chokes.

Martin