How do I fix this hole in 1960's stucco exterior wall?
It looks like a few pieces of wire are at the edge of the hole, straighten these out so they poke towards the center of the opening. Add a few screws to the sub siding, the screws don't need to go through the wood but are for the patch to hold on to. The hole only looks to be about 2" if this is the case a few screws and some of the wires should be enough to hold the plug in place , if the hole is larger you may want to add some expanded metal mesh or wire in the hole. I like expanded mesh but it is harder to work with. Tuck the edges of the wire/mesh in at the edges of the hole using the screws to hold off or away from the wood about 1/2 the depth. Sometimes I will chip the edge closest to the wood to provide a lip and access more wire this helps the plug to hold in place and provides a fresh edge. Mix your patch up and pack into the hole making sure to work the mud into and through the mesh/wire pressing out all air bubbles. Matching is the toughest part, it looks like a heavy spatter was used you may be able to use some of the patch and add a little extra water and a small putty knife load the knife and flick it at the patch, if you like the way it looks let it dry and paint if it needs more repeat the flicking , if you don't like the way it looks wipe it off and try again.