There isn't much here other than the AFM procedure. I'll give this more thought when I get a chance.
Everything here is from the references shown below, with a few comments in an alternate color.
There are no cockpit indications of a tailpipe fire. The most likely method of alert will be from ground crew. Confirm affected engine with ground crew before taking action.
Gulfstream GVII-G500 Airplane Flight Manual, Revision 4, August 29, 2019
Gulfstream GVII-G500 Production Aircraft Systems, Revision 3, July 15, 2019
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