Be very careful about trying to wire the pump directly to 12V.
I cant imagine how running a pump one direction lifts the hood, and running it in reverse lowers the hood! (I am a hydraulic engineer, so maybe thinking to deep into it). Normally running a pump in one direction generates flow and pressure, reversing the pump normally destroys the pump
Would need to see inside pump unit to be sure, but if it uses a reservoir of oil i doubt the pump reverses!
as there is only a black and a power wire to the pump
I would suspect that the pump unit needs earthing to chassis, then I could see one wire runs the pump, and the other wire reverses the direction via a valve...
So power to pump only raises hood, power to pump and reverse wire lowers hood.
Of course that is how a hydraulic engineer would do it, but MGR????
Peter