Water pump stuck on even when engine is off

[azev]

Hi Guys, Just gone through replacing the electric water pump and thermostat on my x5 (the hardest water pump job in my diy career btw).
Anyway, I've follow the bleeding process I found in this forum, by turning keys on, temp on max heat, and low fan then press on the gas pedal 12 sec.
The new pump works great and it start cycling the rpm until it just stuck on max rpm.
I didn't remember how long did I waited before I've decided that the bleeding is done and I get a continuous stream of water from looking at the reservoir.
What I did then is shutdown the ignition and the water stop.
Next thing I did was turned on the engine and let it idle for almost 20min checking for leaks and stuff and everything looks good.
When I turned off the ignition though, the water pump stays on.
A couple cycle of starting the engine and shutting it off, finally stops the pump from going when the ignition is off.

I did a test drive for about 30 min and when I got home and turned off the car, the pump stayed on again. I tried cycling the engine a few times but this time the pump does not want to turn off.

At this point, I unplugged the battery to make sure it didn't drained it.

Any suggestion on what may be the cause and what to look for ?

I am hopping tomorrow when I plugged in the battery the pump is stop running, but if its still running I am lost on what to do next.

Any help is appreciated it.

Thanks