How can I tell what kind of paint is on my stucco?
DO NOT ever use elastomeric paint on stucco.....Stucco needs to breathe.... in truth stucco should never be "painted" at all.  It needs to be lime washed or mineral coated.  This actually bonds chemically to the stone and will breathe, not mold/mildew because of the alkalinity, and fill in small cracks. Minerals can last 50+ years, Lime wash less.  Also you need to know what the stucco is made from, Lime, Portland cement, ???  that will determine what will bond to it.  The lime wash is super inexpensive but doesn't last as long as the mineral silicate.

The new mineral paint will adhere to previously painted stucco.
check out ROMA BIO or KEIM.

Power wash it hard then mineral coat it, they now can match color, it will be beautiful.  Also the mineral coatings slightly reflect light so the color has life like the sun is on it.  

I learn all this when I bought a untouched 1920 stucco house. 

BTW elastomeric paint is forbidden to be used on listed historic buildings as they found that it causes them to mold.  It traps water.  check out the GSA guidelines and united masons websites they go into detail what should be done.