BMW E61 Hydraulic Pump replacement instructions ↗
Illustrated E61 Touring tailgate pump swap: prop the tailgate fully open, strip the right-hand cargo trim, unbolt the pump, then refill the cylinder with a syringe while cycling the tailgate. Rated 3/10, about 2 hours.
Tools mentioned: T20/T25 Torx, 7/8/10/15 mm sockets, small and medium flat screwdrivers, 5 ml syringe