Can my "underage" partner be included in a retirement visa for Thailand?
If so, how do I go about doing this?
Assuming underage you mean younger than the 50 year minimum retirement age requirement: Yes. You will have to provide proof of dependency status, which is usually a marriage certificate.
If you are not yet in thailand, each person needs to be able to enter on their own passport. In other words, each dependent over the age of 15 will need a visa or qualify for Visa Exempt stamp. You did not mention what country you/your dependent is from.
When you both are already in Thailand, then you do this when you apply for an extension of stay (not visa) at the local immigration office. Only the retiree needs to provide the proof of income, not the dependent (either 65k THB monthly or 800k THB seasoned in Thai bank for 2 months for first application, 3 months seasoning for each renewal).
If the dependent becomes 50 years of age, you can still opt to have one of the persons be a dependent of the other retiree. No requirement to do separate retiree applications (and have separate proof of income for each retiree)
*I recommend updating the question to say "younger" The word underage can have other more negative implications.