The trigger in on the dmm6500 is 5v logic.
Your GPIO might be 3.3v, so you’d need an interface for that.
something like : https://www.sparkfun.com/products/12009
The default mode of the trigger is falling edge from 5v to zero.
Depending on what you want to do, the TSP script environment in the DMM might allow you to implement some of the automation with the dmm.
Info: https://www.tek.com/en/video/product-features/what-is-tsp
