Am I eligible for a residence certificate on a 60-day exempt stamp to transfer my scooter in Thailand?

You really need to sit down with someone officially or apply officially, that’s when the rubber meets the road.

Might even be good to take an interpreter with you.

Everyone’s situation is different. I’m working on a motorbike license right now and was told by the driving school to take my girlfriend for my residency certificate , since she is my TM30 contact.

The school told me it will probably go much smoother and will able to address any issues while sitting right there or know exactly what to do next.

I’m in the Nakhon Si Thammarat area.

By the book you need to have stayed longer than 3 month on a long term visa (NOT tourist), to be eligible for a residence certificat.

But not all Immigration Officers have read the book of rules lately.

No, no one can tell you. You didn't include any information in your post so no one can tell you.

Each immigration office has different policies on who can request a residence certificate and who cannot.

If you're in Bangkok then you wouldn't qualify. If you're in Chiang Mai you would. Etc etc