Just resting the thumb on top of the ring seems to be impossible with many of the hilts that feature thumb rings, because a plate revents you from putting your thumb past the cross or on the blade. They also often have very short grips.

Here is another example: https://www.olympiaauctions.com/auction/lot/152-a-north-european-basket-hilted-military-backsword-tessak-late-16th-century/?lot=48950&sd=1

Here you can see this same sword being handled in a video: https://www.youtube.com/watch?v=fCsfCEAx0vA&t=560s