I was having the same problem, could also replicate with plugging in a USB device which gave me an idea and solved the problem for me.
I was getting a stutter every 60s where GPU utilization dropped to 0, but only in FFXIV. I unplugged all USB devices and reconnected one at a time, giving them each a few minutes. They all gave the initial stutter, but leaving them for a few minutes isolated the problem.
My USB microphone turns itself off when not in use, but whilst in that state it is sending a signal every 60s that triggers the same game stutter as connecting a USB device. If you have any USB devices that turn themselves off when not in use, see if disconnecting them fixes your problem. Or alternatively see if you can find a way to keep them turned on if you want to keep them connected.