check the wiring on that adapter youll find that from the OE connector side only two of the pins have wires , the ground and the low side relay power . the fan side of the adapter is wired to ground and the yellow and green wires of the fan and that gives you high speed on the fans ,puts a lot of load on the OE low relay and if it fails the high side switch (224 * overheat safety switch) on the intake will turn on the high side relay but it wont turn the fans on because its not connected to the fan with that adapter
i usually run the RTX hotwire which uses an OE connector that you must install on the fan harness or on the cheap cut the OE connector off the old OE fan and then wire it to the dual fan running the yellow fan wires to low side (A) and green wires to high side (B) and black ground (and a brown on some dual fans with 4 wire plugs ) to (C) then it functions in low and high as the original fans did