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Have you checked that the battery terminals are secure and free from corrosion? Also, have you checked the engine compartment fuse box for signs of corrosion or damage?
If you have a multimeter handy, try measuring the voltage from the 'live' side of the demister with respect to a known good earthing point. The bolts for the boot striker plate are usually a good bet, though I'm not sure whether they're accessible without removing trim.
If there's a high resistance in the supply side, then you should see the voltage pulled down well below 12v by the demister element. If you see 12v or more instead, then it does look like a bad earth is to blame. You can confirm this by measuring the negative side of the heating element with respect to the good, known ground.
That should at least narrow down the possibilities a bit, though I'm not sure where to take it from there. This does sound like an odd one.
Currently in Horatio's garage:
2010 Laguna III Initiale.