What is the process for applying for an annual visa extension based on being married to a Thai spouse without an online appointment?

No problem applying for an extension without a booked appt. Sadly, the wait is the wait and there's no one that can tell you how long it will take because that depends on how many people are in section L-1 (the retirement/marriage section) on the day you go.

Obviously Mondays and Fridays are worse than Tues/Weds/Thurs.

People start showing up there at 5:00-5:30, to get in the main door of building B, then sit in the 200 chairs down the side of immigration office. After those chairs are full people queue up based on the signage.

So unless you wanna go at the crack of dawn to secure a low number outside the immigration door, so you can get in and get a low queue number inside for L-1; I'd say show up after the zombie horde gets in the door, around 9:00-9:15 or so

OR conversely,

go in the early afternoon 1:30-2:00 once they open back up from the lunch closure. Some people said that is the way to do it but some go in the mornings

After that you just wait it out. If you get a queue you'll get served that day

Sorry couldn't be more specific but that's about how it is out there every day

Oh and just so you know, you can make an online booking a month in advance, so next time you're going to do it set a reminder in your phone a month before you wanna do the extension and make an appt when it goes off. Those spots book up FAST now because everyone knows it's way quicker than just showing up.

One last thing you can keep checking the online queue web-portal, because if anyone cancels an appt it will come back up as available for booking and sometimes slots pop up

Best of luck with it