There are many ways to store or build in a hidden switch for your garage door opener.
2008 Mazda Miata MX-5
My 2008 Mazda Miata MX-5 has a small storage bin low on the left side of the driver that is the perfect size for a garage door controller. The only problem is the rattling of the plastic garage door controller. This is easily fixed by cutting a piece from a non-slip dash mat to fit inside the storage bin. I bought the non-slip dash mat at Walmart.
2006 Mazda Tribute
I added a push button switch from Radio Shack to a blank switch location on the left side of the driver in the Mazda Tribute. The small pocket style garage door opener was modified to add wires to the switch and then is hidden inside the dash behind the switch. On other garage door installations i have removed the garage door opener battery and wired the garage door to the car so that it only works when the ignition switch is turned on.