Light-Green + Orange could be for wiper motor or wiper/washer switch.

Green + Yellow could be for rear windscreen heated rear screen switch.

... if you have them.

Well, there you go... I've been proven wrong again.
You actually can lose wires in the interior when swaping engines.
Go figure.

Apparently when I broke the old switch (yes, I absolutely have a white, plastic switch bolted to the brake pedal assembly that actuates the stoplights) I snapped clean off the top half (with all the electrical connections) and left the plastic half with the plunger behind on the pedal. Then, when I lifted the cabin heater box, I trapped the (still connected) top half of the switch on top of the heater box - that's why the circuit was complete. I was thrown off by the presence of a green/orange wire with the correct terminal plug - I figured that was one of the wires and the diagram was incorrect (as I've heard can happen) in the Hayne's book aka "The Blue Book of Lies". It wasn't. I don;t know WHAT that wire goes to yet, but it's not part of the brake light circuit.

I dug around on top of the cabin heater box, located and retrieved the broken plug, found the green and green/purple wires and connected them to my new switch and all is well - thanks so much!!!

Yes there is - you just need to think beyond the 60s.
It is a white plastic device fitted to the pedal box, and can be an utter bugger to set up.

The wires are 90° spade connectors iirc, and I have a sneaky suspicion that the switch is break-to-operate rather than make-to-operate, which would explain why your brake lights are on with everything disconnected.
To set it up properly you need to have the switch positioned exactly right so that the switch operates and the brake lights come on the moment you touch the pedal - this can take several minutes of fiddling with an assistant watching the lights from behind.  It can often change position when you do up the locknut so recheck afterwards.  It's easier to do with the heater and demister pipes removed.

When you removed the broken switch did you remove the wires from the switch or were they not connected at that time ? What year is the car ?

Sorry Cupcake - I've changed mine twice.

13H3735 Brake Light Switch

There is no such thing as a brake light switch. There is brake failure warning switch. This switch is activated if the brake hydraulic pressure is zero, ie when there is a leak in the brake hydraulic sysstem.

My Belgian-built mini has only the plastic 13H3735 switch & it's associated BMK1903A locknut on the brake pedal, no hydraulic switches.  It seems to me that if the pedal switch broke, then the wires must be dangling behind or near the pedal. 

Crawl under there and look up under the dash?

Does the car have a hydraulic brake lamps switch on the brake line connector for the right front flex line, located on the subframe down below the clutch arm?

Since minis have been made for more than 55 years, it sometimes helps to know the year and model of the car prior to trying to imagine what changes have been made to the car since it rolled off of the factory floor. My dad used to joke that if BMC ever built two cars alike, they sent someone out to change something on one.  There were cars shipped with a mechanical brake lamps switch on the pedal box operating the brake lamps, but still had the hydraulic switch as part of the connection for the flex line and front brake pipe.

First question would have to be; Did the brake lights operate properly before the engine swap?

I would find it hard to believe that you could "lose" the wires at the pedal switch. I can't think of a reason to disconnect them during an engine swap.

Perhaps the mechanical switch at the pedal was a temporary repair by the previous owner. Is there a pressure switch located on the subframe near the clutch end? If so, either the switch failed in a "closed" position or someone just spliced the two wires together at that point.

After installing a new engine (long story), I was hooking up electricals and noticed the brake light switch on the brake pedal in the cabin was broken. Ordered a new one and went to look for the wires but I can't find them (WTF?). According to the diagram, the lead INTO the switch is a switched green lead that goes into the cabin straight from the fuse block, and the electrical current OUT OF the switch is carried to the tail lights by a green/purple wire. Right now NEITHER wire is connected since I can't find either one.

Here's the thing... when I switch on the ignition MY BRAKE LIGHTS ILLUMINATE. According to the diagram, this is impossible, since the only way for current to flow into the green/purple stop light wires is via the brake switch.

I checked the tail lights by switching the ignition off but then turning ON the main headlight switch and as expected the tail lights (not the brake lights) illuminated. Switching on the ignition immediately illuminated the stop lights, like there's a direct connection between the hot, switched green lead and the green/purple (which I can't see how happened).

I tried tracing the wires from the tail/brake lights but they go up into the LH rear a-pillar (behind the gas tank) and I cannot follow them. It appears as if the green/purple wire reappears on the LH side via the front a-pillar hole and then passes through the firewall right near the wiper motor. Beyond that all the wires are wrapped in tape and can't be seen.

Ideas? I can snip the green/purple wire up front near the a-pillar and then splice in a new lead to the brake light switch (along with a second, green lead to the switched hot), but I hate the thought of having some weird, random (possibly still hot and short-able) connection somewhere inside the harness...

Thanks! --Matt