I couldn't speak of that border nor recent times but the last time I did a border bounce, I crossed over had lunch came back. The border was Nong Khai and it was pre-covid.
I am looking at different visa options now. The requirement for a tourist visa, "Document indicating current location (driving license, bank statement, or proof of stay)". I have a driver's license and passport from the US. Driver license and Bank Statement do not indicate current location in the strictest sense of the word, and are acceptable.
You got bad advice. I realize (now) the first page of what appears to be the application process asks "current location", but that isn't actually part of the visa process. In the actual visa process the two questions are worded differently, "Where are you permanent resident" and "Where is your passport from", of course they are worded differently. Regardless of where a person is actually, does not change the answer to those two questions. Hence, you don't even have to lie.. But none the less, they don't check your physical location, the look at your flights. For me it was sufficient to show a flight into Thailand, (Once I was in Mexico, Once I was in Indonesia, later this month I will be in the Philippines).
More practically, You take a risk. You take a similar risk if you apply in person with all the correct paperwork. The embassy can always deny you a visa for any reason. Your risk is $60/USD. I would encourage you to fill out the application online, answer the questions, submit the various paperwork they request, and before you make payment (the last step), at that point evaluate the risk, rewards and other options. I think you will likely find the $60 risk worth it.
Absolutely they can apply for a eVisa while in Mexico from the Embassy of Thailand DC. I am a US citizen and applied for a visa while in Mexico. The first page is only there for entertainment purposes. The embassy will want to see flight details to Thailand and I would recommend showing US to Thailand if possible (a lot of Flights from the Americas route through US).
I am a US citizen and therefore I use the US Embassy and they don't exactly offer a 'free to marry' certificate. They provide and affidavit. The affidavit does not specifically mention my wife. Which means I could have changed wives.
Can we use Myanmar to do border bounces? Last time I did that it was just before Covid. I had taken a bus up to kanchanaburi and I found people handing around the bus station that will shuttle you to/from the border. Once I exited Thailand there were people hanging around that had taken my passport into Myanmar and returned an hour later, cost like 500 baht or something. There is a restaurant to sit and wait.
Effective, I left Thailand and never entered Myanmar but my passport did enter Myanmar.
There were several foreigners there waiting for their passport to be returned so I figure it was safe.