This little guy is hanging around on a prickly ash my son has growing in a pot.

Could that be one of the Tiger Swallowtails? Not sure whether it would be Eastern or Western where you are. They're known to like ash. Hard to tell from your photo, but this might give you a start to some research.

https://www.insectidentificati...

Thank you, what might be a better photo?

Wait, I took a closer look...what I took for lack of focus was the white markings.
Pretty sure you have a Giant Swallowtail. Way cool!
https://www.inaturalist.org/gu...

(Helps to wear the reading glasses...)

Thanks @NMoasis it looks like its been eating some of the ash leaves.

Keep track of and maybe you'll be lucky enough to see it pupate. Here's a good article and pictures about its lifecycle
https://entnemdept.ufl.edu/cre...

Great article, I believe the tree he has in the pot is Hercules-club, Zanthoxylum clava-herculis L

Wow, this keeps getting more interesting!
https://en.m.wikipedia.org/wik...

I need to move it to one of my 15gal pots but don't want to disturb the caterpillar.

If the cat is active (vs not yet beginning to pupate) gently hold a small stick against its front legs in line with the branch it's on and it might crawl onto it. Then you can place it somewhere safe and return it to the tree when it's potted.

Good idea, I just checked and there looks to be a thin thread of silk attached to a tiny branch. I noticed that it has really been busy eating leaves.

If there is a thread, it should have stopped eating. The thread is created to secure the chrysalis to the branch. Here's an article about breeding them in enclosures that has some excellent photgraphs of the chrysalis formation. Follow the various links for related articles and more photos. As I see it in the photos, the initial stage of the chrysalis still strongly resembles the caterpillar... but it won't be eating.
I have a black swallowtail that went from looking like a caterpillar to being a fully-formed chrysalis overnight, easy to determine what stage it was in. I've never seen a Giant ST in real life. So envious!
https://monarchbutterflylifecy...

Thank you for the link, it has moved quite a ways from where it had been feeding.

That soesn't sound like it's pupating.

I don't think so either, it's just sitting on a leaf. Hopefully it'll hold on during this bout of rain we've got forecast.

Can't find the little guy this morning

Ever end up seeing it again?

No, I'm wondering if the city deer we have may have eaten it up while munching on the tree.

Sadly, there are so many survival obstacles to caterpillars, I think it's amazing any survive at all. About 10 mature BST cats disappeared from my garden during the Heat Dome double whammy of 100+ degree days and wild high winds. Or a roadrunner ate them. Or maybe they crawled into the shrubbery to pupate (my hope). And those were the ones that looked like they'd made it!—having avoided being eaten when they were the size of a pinhead.

I'll add to my thread, another caterpillar showed up, very young one. I remember seeing one of the giant Swallowtails by the tree a few weeks ago possibly laying eggs?