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Not eligible
The Working Holiday Scheme is limited to people aged 18 to 30, and the limit is applied at the date of application with no discretion attached to it. If you are over thirty, that route is closed, and no amount of qualification or funding reopens it.
What is worth knowing is that the working holiday visa is one of the weaker things Thailand offers anyway - twelve months, no extension, no renewal, no route to residence, a three-month cap on working for any one employer, and liability to Thai income tax on what you earn. Several of the routes open to people of any age are better.
If you work remotely for a foreign employer or foreign clients, the Destination Thailand Visa gives five years rather than one: multiple entry, 180 days per entry, extendable once per entry inside Thailand by a further 180 days, on THB 500,000 in the bank - which most missions want to have been there for three months. There is no age limit and no employer test. For most people who were considering a working holiday, this is simply a better product.
If you would be working for a Thai employer, the Non-Immigrant B visa and work permit route has no age limit either. The constraint sits on the employer, who must hold THB 2 million of fully paid-up registered capital and employ four Thai nationals for each foreign work permit. Unlike the working holiday visa, that route leads somewhere: three continuous years of extensions opens permanent residence, and five years of permanent residence opens naturalisation.
If you are coming to train or study - Muay Thai, Thai cooking, medical treatment - the Destination Thailand Visa's Thai Soft Power stream covers it on the same five-year terms.
And if you are fifty or over, the retirement routes ask for THB 800,000 in a Thai bank or THB 65,000 a month in income, which is a lower bar than people expect.
What happens next: pick by how you earn rather than by how long you want to stay, since that is what actually determines which route is open. For most people under fifty who are not employed in Thailand, the Destination Thailand Visa is the answer.