Does anyone know if it is possible to use a custom Google Analytics Event Goal as a trigger in GTM? If so, how is this able to be executed?
No, not as such. If you have destination goals you can just use a pageview trigger with the given url, or if you have event based goals you can use the same trigger in GTM that sends the event to GA (although unlike GA goals the triggers can fire multiple times per session).
But there is no real connection between GA and GTM, so you cannot use GA data to control GTM (if you have Google Analytics 360 and Google Optimize 360 you could presumably set up an A/B-Test with 100% participants that pushes GTM events to the datalayer based on GA audiences, but that would incur a six figure yearly fee).