FADEC Power
FADEC's (or EEC's) are normally powered by a dedicated little generator, driven by their own engine.
Do not mistake that little power source for the normal engine driven generator!
The EEC generator (or alternator) will deliver enough power already at very low engine RPM (so also during windmilling airstarts). It will usually have separate coils for the two EEC channels. Often the electrics needed to carry the signal from thust lever to EEC are also powered from that generator.
In other words, even with the most complete electrical power failure on board, the engine control should still be unhampered.
Only as a backup to the EEC alternators will there be a connection from aircraft electrical system to EEC; on the ground, before engine is turned by the starter, could be an example of aircraft electrics powering the EECs.