yes your right BUT only need go to neighbouring country and I'd say less than a week from what i see daily, many in the group give details of where they went and how it went to.
I suggest you come with a travel cover to start, then ask around expats and talk to brokers. Medical insurance are annually so not sure suitable for you and much more expensive as they don't send you home for surgery but take care of you here, very different
it would need to be passport number, many western insurance brokers here to help you. First maybe come with a travel insurance for 1 or 2 months, then gives you time to change and set up suitable policy for a Thai health insurance. Be careful on max per night for hospital, many thai policies only pay to 3000 baht, enough for government private room or upcountry hospital but should you be staying in a tourist area and require private hospital which all have private rooms and english speaking staff you need 6000 a night cover