We were recently looking to call some REST APIs (like hitting a Hadoop cluster and running a custom task in pig or spark) from JMP/JSL... and ended up using the Open function with a custom URL that gets generated from user inputs. This is similar to what can be done manually using File -> Internet Open with the 'Open As' set to Data (as pointed out by many Discussions). Our REST API returns CSV/TSV formatted text that is easily imported by JMP.
Reminder for my future self... of this features available in JMP 13
The Internet Open Timeout preference on the General preference page applies to opening web pages with the Internet Open feature. JMP waits the specified number of seconds before stopping the import due to an error. 60 seconds is the default value.
and the new http request function coming in JMP 14.