Does a re-entry permit apply to visa-exempt entries in Thailand?

I see people talking about a "re-entry permit" do do with various kinds of visas, but not sure if it applies to a visa-exempt situation. I'll have a new visa-exempt entry stamp soon, will be here two weeks later, for a few weeks, then back for another two weeks before flying out. I could just get a new visa exempt entry when I come back, but that would mean I've used 2 for the year at land borders already. A re-entry permit would allow me to get another land entry later in the year.

Again, I'm not sure if it's even applicable to the visa-exempt situation, so that is the first question.