I think where the confusion starts is that there are (2) white wires he’s dealing with. One is the switched source for the FiTech that is connected to the ballast on the 12v side. The other is on the wiring to a standard Bosch style fan relay, and in his case is also a switched source. That is the wire that will be to the battery, (or jumped to main power at the relay), as the FiTech supplies the ground for the fan relay.
