What are the requirements for obtaining a non-immigrant O visa for a couple of non-Thai citizens in Thailand?

I'm on a dependency visa.

To get this my English wife holds a none O visa based on retirement.

We then had our marriage certificate verified by the British embassy and then translated into Thai, which was then verified by the ministry of foreign affairs which was all done whilst being in Thailand.

The intention for allowing a „dependent visa” was and still is, mainly based on the “dependent partner” not having to show his/her own financial proof.

However, many embassies have discontinued to issue “trailing spouse” or “dependent” Non-Imm-O visa to partner married to someone who holds a Non-Imm-O retirement visa or an Extension of Stay based on it.

You need to ask the Thai Embassy where you are applying, on how they do deal with it. And keep in mind – even if the Embassy issues the dependent visa. It is not guaranteed that Immigration accepts it for an application to a 12-months Extension of Stay. Immigration could still ask you to have two separate bank account with 800K Thai Baht on it from each of you

The reason you can't find the application online is because embassies pretty much all stopped offering this visa years ago. Now each person will need their own visa and own bank account with proof of funds.

There are a couple of caveats. Some embassies will let you do it if one spouse has a non-OA visa (but then you have to purchase the mandatory insurance).

There's also a VERY convoluted workaround you can do while in Thailand. Your wife would have to get to Thailand as a tourist. Sign up with a school and apply for an education visa. They would need to study for 3 months and then continue for another 3 months so they also apply for the first 90-day extension. This will put your wife onto an extension of stay that was based on a non-immigrant visa. This would then allow your wife to apply for an extension for a different reason (trailing spouse extension) after 6 months.