I'm attempting to replace the throttle cable because it broke on the carburetor side.

Are there any tricks to removing the ball socket? I've tried to pop it off with a screwdriver and no luck.

Use the 8mm jam nut and turn it like you're trying to tighten it, it should pop off

Tighten it until it pops off... Opposite of what I would expect. Thanks, will try that tonight

Use a 7 or 8 mm thin ignition wrench and put it between the ball stud and socket and pry it off

Okay, so I got the dumb thing off easily enough. What's the trick to putting that ball socket back on?

Push hard

Ha. Touche

Wrong end of a screwdriver, something to push on it that's harder than your thumb.
Or tape up some pump pliers.