Brian,
I suspect that the reason you are stumped is that the device is bad.
The Asian Adapter that Don mentioned is supposed to be in the Curt device - according to their specifications.
Why? The simple answer is that some vehicles have what are call 3 filament taillights (your Madza) and others (your trailer) have two filament taillights. If a vehicle has only one bulb that is a dual filament and it does stop/turn/tail, that is a two. If it has two bulbs (usually in an amber turn signal, that is a three.
Inside that little box is a collection of electronics to make everybody work together. It seems that they are not. If you point your browser at www.curtmfg.com and look for support on Monday, you should be able to get someone to tell you it is defective and where to ship it.
Good Luck
Matt