I have rented a scooter several times in Krabi in the south of Thailand. They don't really care about your license.
As a general rule, you can use your EU license abroad for a stay of up to 3 months. That is true in other countries that have more strict laws like Australia. Beyond 3 months, officially you must get a local license.
As for Thailand specifically, the country relies very much on tourism, and people are usually very "kind" with tourists. I think the authorities would not be too annoying if you are not fully compliant with whatever laws related to your bike (I.e your light dysfunction or your insurance missing). As far as I know, there are mostly 2 things you really should comply with in Thailand, it is to not consume drugs and not say/write something about the King. Or you would put yourself in very very serious trouble.
In Malaysia, I drove my Honda wave (125cc) for years without insurance nor license. I never had any serious issue. I was driving everyday to any place in Kuala Lumpur, and taking highways. The police would usually not arrest foreigners (I mean white foreigners).
I was arrested once by the police on the highway. They were behind and didn't see my face until I stopped the bike. They probably assumed I was a local as there are very very few Europeans driving bikes in Kuala Lumpur. They clearly looked upset to see they arrested a European dude, but had to go through the process. My bike was fully functional and I was wearing a helmet. I just didn't have any license nor insurance with me. I just had a local car driving license which doesn't allow you to drive a 125cc bike (I always thought a car driving license was good enough until that day). I got fined for that. My Malaysian friend sitting behind me on the bike was laughing all the way during the arrest. She told me not to worry about that because I would be fine not paying the fine. The fine was of RM 200, which is 40 over euros (rather kind compared to what you would get in a similar situation in Europe). The 2 policemen went through the official procedure of writing a fine and didn't ask for a bribe.