Yogis would be Hermit or HPS...
omg yes thirteen, antsy is definitely a way to describe the person in that picture. it totally fits. and the stillness of 4 is temporary anyway. water is gonna move (evaporation is a kind of movement, is it not?).
Not according to the cards
The cards are magic/art/poetry not science. Water that evaporates means "emotions" vanish. Water stagnating means emotions turn poisonous.
(...do yogis actually sit there all time when no one is looking))?
Likely not as bodily functions usually require some movement. That said, there are stories of holy folk around the world who stayed in very small spaces for decades on end. St. Simeon lived on a platform high above the city for 30 years (his needs attended to by those who brought up food, water, etc). And there were monks/nuns known as "anchors/anchoresses" during the middle ages who literally had their cells walled up and never left again. They, again, had small windows and were attended to by fellow monks/nuns bringing food, water, etc.
These holy people, by remaining stationary, became a living connection to the divine. As all they did was meditate and pray, they were viewed as having a special link to the spiritual. And so supplicants would visit them asking for advice, or for them to pray for them, heal them, etc. (That's where you get that old joke about the guy climbing the mountain to ask the bearded Yogi living on the peak: "What's the meaning of life?"). But none of these sorts are 4/Cups. The Cup suit is about spirituality, but more in the mold of the seeker on a quest (holy grail, right?). This as compared to the philosophical, argumentative Swords, the Crusading, preaching Wands and the solidly, brick-and-mortar, By-the-Book Pentacles. Meaning, a Cup card, spiritually, usually indicates the person is on pilgrimage. Sailing to see new holy lands and places; the desire to feel emotionally inspired.
As for those yogis or St. Simeons or Anchoresses, they're Hermits and High Priestesses. In the case of the Hermit, knowledge is found by staying in one spot, allowing the seeker to really focus, and not be distracted by other people or changing scenery; this allows them to re-examining all that is known, and find the truth. To really get it right. In the case of the HPS, who is connected to the Moon and water, information flows to her and through her. Which is why she doesn't need to move like other water cards.