Not sure how long this function has been around, as I am fairly new to JMP, and I just found this function myself while trying to solve a similar problem, but it seems that the function "Include File List()" returns a list of open files that are in the context of the executing script. (By the way, the description of this function is only sort of informative, as is the case for most functions/methods/messages in the Scripting Index or online resources.)
It seems that if this function is run at the top of the script before anything else is opened by the script that the script file path and script file name can be extracted from that as this is the only path returned at that point.
When I tested it with other files open in JMP, and ran the script by double clicking it from Windows Explorer (with the script set to run on open without opening a script editor window by including "//!" at the top of the script), I get only the path of that script returned. None of the other opened files are returned.