Fuse 8 also feeds the internal relay that feeds the regulator [and other things: ECU x 3/EGR/MAF/etc.] with 12v.
Does fusebox terminal C8 become live when cranked? That's where it all comes from.
If not; try feeding C8 when cranking.
C3 and C13 seem to be the BM34 to ECU comms links - are they OK?