Walk-in appointment wait times at Travis County Tax office for vehicle titles?

I’m selling my car, private party. I want to do the transaction at the tax office, to get everything wrapped up and ensure the buyer has registered the car in their name. That’s how I’ve done it before, but that was deacdes ago in old Austin. In our New and Improved Austin, the Travis County tax office vehicle title department has no appointments for the next 22 days.

Has anyone done walk-ins for that department recently? Their website says they close walk-ins once they are capacity.

It’s a cheap old car so I don’t want to drag this out with getting a deposit and having the buyer return with the balance and temp tags. And, for the price, I’m sure they won’t want the hassle either.

I guess I can follow the buyer there, remove the plates and registration sticker, and then let them wait on their own. If I’ve done a bill of sale, a Vehicle Motor Transfer notification, cancelled the insurance, and kept the plates and registration sticker (no toll tag), there’s not any actual liability for me if they delay in registering it, just a headache presenting all that documentation if something was to happen and they had not registered car in their name… still, I’d rather have it all tied up day of sale if possible.