OK, but nobody here has claimed that “a think” means the same thing as “a thought”, Mite. You’re correcting a mistake nobody has made. We understand already that an individual thought isn’t the same as a period of thinking/of consideration.
That’s why people would be unlikely to use “think” as a noun in your earlier example sentence about the museum parking. Not because it isn’t a noun - but because it wasn’t a fitting example. You had the wrong idea about the type of noun it was.
And if you think “to have a think” is incorrect syntax, you have another think coming.
You may not like it much, but the syntax is perfectly sound.