Will I get stopped in Thailand if my Emirates insurance is only for 30 days while I stay for 120 days?

What stamp are you entering on? There's nothing I know of that's exactly 120 days. Knowing what visa you have or no visa will help answer the question.

It's tricky. There was an interview Richard Barrow did with a top official last month where they said insurance should really only be needed for the first 30 days because that's when you'd be tested and possibly hospitalized for Covid.

But immigration has generally made their interpretation of the rule that you should have insurance for as long as you are stamped in for.

There are reports that some people have been able to enter with only 30 days of insurance even on longer stamps, but it's possible you could be stopped also.

In all cases you'll need a certificate so did you get the certificate from the Emirates insurance carrier?

If you're coming in on visa exempt and you have that, you have nothing to worry about. But if you're coming in on a long entry like tourist visa or something longer, it may be an issue.