I decided to take a crack at this tonight and wanted to share photos of my efforts. I recently installed an M5 shift knob/boot so I have the stock boot laying around for practice.
I started by picking out the thread for the job, which was harder than I expected. Matching the M colors was a bit tricky since I didn't have an official BMW pattern to compare against. It also didn't help that I was at Joanne Fabrics at 9pm and couldn't compare the thread in daylight.
I picked an embroidery thread because it was thicker than the machine thread. The thinner threads didn't seem to give the right look. You stitch one bank in red, the other in light blue, and then the dark blue goes between those two. Dark blue doesn't thread through the boot itself at all.
This is the pattern described by the OP, it's really quite simple. This view is from the inside of the boot, and the dashes represent what you're doing on the back (visible) side. If the holes are numbered from start (1) to finish (n) you're going 2, 1, 3, 2, 4, 3, 5, 4, etc.
This is where I ended up after a short trial. The thread doesn't look bad, but it's thicker than I like so I'll be re-evaluating my options. I'll keep everyone posted.