You can stop looking for the button....there is none. They do not fold electrically. I have an MX-5 RF GT I picked last Friday, but knew this going in. This is not unlike the Porsche Cayman R I sold last year which also did not have electrically folding mirrors (or automatic headlights) even though a Cayenne I had owned of the same model year (2012) had both.

In the case of the MX-5 I've assumed this is all part of their whole "chasing grams" thing intended to try and balance the need for convenience features while avoiding adding weight. This said, the MX-5 is so tiny both in length and width compared to even the Cayman that I don't see how I'd need to fold the mirrors in anyway. This car replaced my wife's Macan (she now has a 2017 Cayenne to drive) and "her" space in the garage now seems half empty (which is arguably is quite literally).

If you need to, you can fold them in manually.