ILI9325C Screen-off problem

I bought three cheap 2.4" LCD screens, with touchpad and SD card reader from EBay like this one

I want to implement a screen timeout so the display goes off after a time of non-use.
Though the The library I am using from the masterly Henning Electronics - Henning Karlsen does not support LCDon/Off() for this device, so I thought I would cudgel my own solution using a MOSFET to disconnect the power. However, I find I can unplug the 5V, 3.3V and GND and the thing is still awake! I am guessing it is drawing power from the data and control lines of the 8-bit parallel interface?

Anyway - I wonder if anyone can suggest some way to get this done. This display will sit in a plant propagator - on all day every day - and I don't want to wear it out if I don't have to.

Thanks, Chris