How do I identify what my house is built of under stucco
Since you're going to hang something on it, you're going to make a hole anyway.  Just make that hole your test hole, and if you hit wood or brick, it will be pretty obvious with even a small bit.  Then get the appropriate bolt/screw for the wall, expand the hole as necessary, and do the install.

I'd recommend against checking from the inside since the first thing you'll see is wood sheathing even if there's brick outside (unless you're as unlucky as me and see sheet rock installed behind aluminum siding, but I digress).  You'd have to go through the insulation, through the sheathing, and through the house wrap, to see if there is any brick or other material before the stucco.  At that point, there's a good chance you'll punch a hole right through the stucco anyway.