I will be doing a masonic cake and need to know how to keep the cutouts crisp and how thick they should be

you can make them any thickness you want -- to crisp them up -- you can use tylose powder or cornstarch kneaded in -- make them days/weeks in advance so they can dry --

best to you

As K8 said, adding tylose or cornstarch to fondant and keeping your cutouts thin when you make them several days to weeks ahaed will cause them to dry crisp/hard.  Do NOT wrap them in anything nor put them in the frig - you want them to air dry.