R53 Cooper S.

I found a youtube video showing installation, but the video did not show removal of the old one; the unit snaps into a bracket, but how is the unit released from that bracket for removal?

Any parts necessary, beyond the washer unit and the external cap; single-use hose clamps, or anything else lurking to make what looks like a ten-minute job an afternoon-killer?

I was driving along, and "something" suddenly bounced off the windshield.  It was daylight, I hadn't washed the headlights recently, but the washer unit spontaneously broke, not just the external trim piece, but the last inch of the washer unit just popped off.  Pretty strange.

I posted this same inquiry at Mini2, and someone pointed me to an online manual.

Though the illustration, showing where to release the mounting clip, was not very helpful - an arrow pointing to the side of the pump, when the clip is actually on the end/bottom as you look at it with the hood open -  it led me to the clip location, and, as I thought, removal was literally a two-minute job, taking more time to assemble a couple of tools for the project than to actually remove the "high pressure nozzle".

That the part is broken at the tip, where the chrome trim piece attaches, is actually a benefit, as I don't have to remove that part from the outside before removing the pump through the inside.

Installation will be installing the hose on the new pump, sliding it onto the bracket, then clipping the trim piece on the tip.

Hoping Seattle MINI has the parts in stock.

This is what you'll see, if you open the hood and look at the washer on the driver's side:

This is the interesting area, which is on the opposite side; rectangular mount in the middle:

This is the clip, which I could almost get to with my thumb, but I used a small screwdriver to gently pry it open so the unit can be slid down - toward you in this orientation - and off the bracket: