The next step is to use your multimeter to measure the current between the 24V trigger pin and GND. Also measure the open circuit voltage between that pin and GND. It may be about 24V, in which case you cannot directly connect the pin to an Arduino output.
You will need that information to choose the best switching device, although a transistor will probably work well.
I would expect a Mosfet is much better than a relay. Even a BJT (aka transistor).
Being a "trigger" input it is very unlikely any real current is needed.
Next question is: What arduino are you using? If a 5V board then a mosfet is the best, if a 3.3V board then a transistor is the best
CAUTION: This will necessitate connecting the instrument ground to the Arduino ground to the ground of whatever else is connected to the Arduino. So maybe for getting started with the minimum of design effort a relay may be the way to go. It should be a small relay such as: This relay