A genuine mauresque is equal parts absinthe and orgeat served in a chilled Collins glass with ice and a small pitcher of icewater, similar to how a pastis is presented. In fact, when absinthe was scarce they would use pastis instead. I believe the pitcher is called a 'broc'.
There are other similar add-ins to pastis that give it some color and complexity, but the thing with pastis, they say, is that the third one is the one that you really enjoy. :-)
I like the name 'mauresque' because it reminds me of Moriscos and Marranos and mozarabs.
And don't get me started on 'turquoise'.