I bought a one week gold account pass and set a pet as my leashed pet, but that pet's image isn't showing under my avatar. I cleared my cache and that didn't help. Any idea what's causing this?

The pet leash only shows as long as you are an active Gold account user and your icon shows blue now, which generally means you GA has run out. If you still have days showing on your GA (you can see your GA status by clicking here), then you will need to submit a Ticket to find out why its cut out early.

You also have to activate the GA from your inventory after you buy the medal, in case you missed that step

I just bought the membership today and did activate it, page linked says roughly one week left. If my pet doesn't show on this post I'll put a ticket in

If you just bought it, it could also be a cache issue

I cleared the entirely of my browsing history including cache and re-logged in but still not showing. So seemingly not cache.

I meant the site cache. You've got a GA icon in the hover over your username, so it seems to be catching up c:

Ah, I see. Awesome, glad it's catching up.

is it possible your pet icon isn't centered?

Make sure that your pets headshot is centered correctly by going to the Personal tab -> Pets -> drop down for the leashed pet > edit headshot (or click here)