I found that there is no way to do this in-game for the gamepad.
en-us keyboard the
N key will activate push-to-talk by default.
However, various utils (depending on your gamepad) can be used to map one of the gamepad buttons to the push-to-talk button (
Since this game makes good use of all gamepad buttons, remapping one of the gamepad buttons for push-to-talk is unreasonable to do, and therefore the best option when doing voice chat with GTAV:PC is to use voice-activated+mute.
Yes, I know that this is the norm for console gamers, but us oldskool PC gamers are used to push-to-talk. It is especially handy for those of us with large/busy households, or who are gaming in public / cafes / etc which is the great thing about PC games: you can play them on a laptop!