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I need a Desk.com ticket to be spawned whenever someone dials either of the two RingCentral numbers that are associated with two of my company's cell phones. Desk.com's support desk informed me that this integration requires an API message from RingCentral.
Using these you can subscribe for the extension presence eventFilter. When you receive events you can use that information to create a case in Desk.com or optionally make another request to RingCentral for more info before creating the case.
You can also use Zapier to create a new Desk.com case whenever a RingCentral call ends. To do this, you can use the "Call Ended" trigger with the Desk.com with the "Create Case" action.