I've done this so many times I can give some clear help here. While the intent of the OP to be helpful by linking that video, that video is not really helpful, as it sets many people who have to go through this job up to damage their column.
The collar with the rolled edge that everyone's trying to force the switch through must come off to do the job properly and without damage hard to replace internal parts. That's the Miller tool that no one has. So, get a 4 leg puller from the tool store - unusual, but not impossible to find like the Miller tool, reverse the arms, use a hose clamp on their other ends to prevent them from "collapsing" away from the rolled edge, and go to work. Use plenty of penetrant down the inside of the collar to allow it to get between the collar and the inside surface the collar is sitting on - it's simply a VERY tight friction fit. Be gentle with the amount of pull you apply with the puller, while gently tapping on the outside of collar to get it to start to slide. Move the 4 leg puller around to apply its force in multiple areas. Again, work GENTLY and slowly, otherwise you will bend that rolled edge.
What the guy in the video also fails to mention is that you have to depress the horn contact ring to allow that big C clip to be removed easily with out wrecking the horn contact ring's molded in ridges that keep it properly aligned. It is held up against the C clip by a majorly strong spring underneath, which needs to be depressed. To do that requires a special tool to do that (also unobtanium), or to make one which is actually fairly simple.
The time it took for that guy to get horn ring out was edited out of the video and glossed over - you can see the damage to the horn contact ring caused by the various tools including a big *** screwdriver. It's lucky he didn't break the horn contact ring.