Can I work remotely on a tourist visa in Thailand and how long do I need to be out of the country before reapplying for another tourist visa?

All the people here that will tell you that you can't are fear mongerers so don't listen to them

They are currently looking at a digital nomad visa but TIT so who knows

From 31 October the 35 current visa exemption is changing to 45 days you can get a 30 day extension at the end of that or just fly out and back again 45 days starts again. It goes back to 30 days march 2023

Technically, it is illegal to do any work inside of Thailand without a work permit and a work-approved visa.

Realistically, as long as you don't advertise that you are doing it, working remotely in Thailand is fine and tons of people do it.

There is no written requirement to be outside of Thailand any amount of time. You can go buy tourist visas every 90 days as long as consulates will continue selling them to you. Eventually the consulates and/or immigration may start questioning why you are spending so much time in Thailand though as a tourist does not usually spend months inside of a country.