All correct. Mostly doesn't matter, but why not connect it like the factory wiring schematic? (search for links here for free download). They generally show the brake switch pictorially, so just match the colors shown.
That's what I typically do but could not understand the schematic as the factory service manual doesn't make mention of where the white or red connector's on the factory harness go. I guess I got fooled about positive and negative hookup and the fact it's a switch so it's only ground open vs closed.
For anyone searching this in the future, I put the input closer to the firewall and output towards the driver. It works perfectly with no issues.
Wish I could say the same for some of my other circuits.