Since the drain is very repeatable, connecting an ammeter in series with the battery and disconnecting each fuse in turn is a good idea as @jphil1618 suggested.
You could find that the problem is associated with multiple fuses, for example it could be the fuel pump that is running (I know you would hear the pump) and while pulling the fuel pump fuse will stop the pump running, it could be the fact that the engine ECU is still powered up and is switching the fuel pump on and off. The ECU may have its own fused supply that is actually causing the problem. So don't stop testing at the first fuse you find that stops the drain.
Post details of what you find.