Horn and interior light - Ignition independant, brown into fuse box, purple out (I think)
Wipers are on the ignition dependent fused circuit, white in green out on the fusebox. I can't remember if the lighting system is fused, but I have a feeling it isn't.
I don't have a Minor wiring diagram to hand right now, and though I should know all of this (having been wiring up the pickup recently) I can't remember it well enough
However, have you got a good connection on the battery terminals? It's possible for them to be loose or dirty, so you'll get low current - Your meter will see 12 volts, but the moment any serious load is put on the system the connection fails. Check the solenoid terminals where the main pos goes to.
After that I'm at a loss, you've got battery power to the loom if the interior light and horn work, but you're not getting any lights (not ign dependent) or anything on the ignition circuit. Voltage regulator? I'm trying to remember what colour the main light feed is, blue and brown? Which I think appears on the regulator (end terminal nearest the wing), which is why I'm wondering if it's something to do with that.
Wish I had a diagram here!