Turns out this is a common problem. Replaced the pump. Used DIY instructions from Pelican Parts http://www.pelicanparts.com/techart...47-SUSPEN-Power_Steering_Pump_Replacement.htm and http://www.billswebspace.com/MiniR53PSPFanDuctDIY.htm Bought a rebuilt pump from BuyAutoParts off of eBay. http://www.ebay.com/itm/290662049259?ssPageName=STRK:MEWNX:IT&_trksid=p3984.m1439.l2649 The part looked brand new. They even supplied a shipping tag to return the core. The constant running also killed my 4 year old battery. I also read there is a chance of fire from the bad pump overheating. Nice.
Hope you replaced the power steering fan as well thats what causes the pump to overheat and keep on running on. That is quite a common problem for the older MINI's. Glad to hear you did it yourself not really that bad of a job to do.
Probably would take me a lot less time if I had to do it again. Hopefully I won't. I didn't replace the fan although I did spin it and felt no binding. I'll consider changing it the next time I need to put it up on jack stands. Next project will be brake pads and rotors.