Buy a 1/4 inch universal clevis pin and then do this:

Here's the clevis pin:

You can buy them here at Home Depot https://www.homedepot.com/p/1-4-in-x-2-in-Zinc-Plated-Universal-Clevis-Pin-815418/204276164 for less than $2.00.

If you don't use one of these, I guarantee that the first time you try installing the pivot pin, you're going to lose your grip on the detent or the pivot pin, and then the pivot pin detent spring, as well as the detent, will shoot into orbit.

If you're lucky, they'll just embed themselves in your wall, at which point you can dig them out and try again.

The exact same thing is going to happen on the second, third, fourth, fifth, and sixth times you try.

For me, the 7th time was the charm.

Alternatively, you can just buy the clevis pin and save yourself the agony of installing the pivot pin without the appropriate tools.

Many thanks to https://jmarcher.io/ for the tip.