Vertical plane cutting through a cone

I’m trying to make a replacement part for attaching the back to an office chair.

There is a cylinder running up most of the way so it can be mounted on a metal rod.

I’ve been able to draw the basic shape by drawing a profile of the part and then using the push/pull tool to follow a circle.

But, there is a vertical plane that cuts through the lower tapered cone. I think it’s used to reference against the back of the chair bracket and prevent it from spinning.

The attached skp file shows where I’m at.
Bob’s chair repair.skp (130.6 KB)

I’d appreciate hearing any hints or guidelines.

Do you want to look together?

Yes, please. Here’s a picture of the vertical plane I was talking about.

PM sent