On an Auris, I have recently made up one seat from two 'bad' ones. The pneumatic-style lumbar adjustment mechanism (air pump and bag and switch) was in the 'new' (breakers yard) seat, but not the old one, and was transferred across. So I have seen some of the Auris lumbar mechanism close up. I would expect it to be the same design in your car as both cars are from the same Toyota plant, and almost certainly the seats are made by Johnson Controls for Toyota, probably nearby (expensive to transport otherwise?).
The inflate/deflate valve and pump are wrapped together in thin grey, vinyl wallet and live at the base of the seat back on the r/h side, on the inside of the major steel side support. On the Auris you can just see this module if the rear seat panel is unzipped completely (the Auris has two vertical zips on the seat back). Just follow the air tube back from the bladder in the seat back.
I had no reason to look inside the vinyl bag to get a view of the motor/valve, as I had tested the unit out of the car before fitting. The unit is quite small and a label says it is made in Poland. It is almost completely silent in deflate mode, by the way, just a single click. It has three wires going to to the pump/valve, I imagine these are 12v. to air pump, ground, and 12v. to air release valve.
Dismantling the seat is actually quite straightforward. Getting the seat out of the car is very tight, but you may not have to! Expect to find some rust on the seat frame, and look out for sharp edges on the steel pressings!
I have no idea of the cost of this part, but this is a Toyota, so I would expect around £1bn + vat. But you may get a small discount if you ask nicely (10%).
This picture is of the seat back without foam etc. as seen from the dashboard point of view.
HTH