The answer is based on geometry and the relevant plots are impossible to draw here but are nicely presented in https://en.wikipedia.org/wiki/Ecliptic. In the figures we can see (with some effort) that the Sun-Earth line is almost parallel (Exactly Parallel at the equinox) ) to the vertical at the meridian so the Sun at this latitude "goes up and down". At the poles it appears to move along the observer's horizon so it does go "left and right".
These are the extreme cases, the apparent path of the Sun in the Sky at latitudes between the Meridian and the Pole exhibits both "Up and Down" and "Left to Right Components" with the latter being more pronounced near the Poles.
Yes, because Earth doesn't orbit the Sun in a perfect circular motion, and its axis is tilted at roughly a 23.5-degree angle to the orbit, it takes a different path across the sky over a day. Earth is always tilted in the same direction in space. But it appears to rise and set because of the Earth's rotation on its axis. It makes one complete turn every 24 hours. It turns toward the east. As the Earth rotates toward the east, it looks like the sun is moving west. The sun rises from the east, on the vast majority of world maps, that's to the right. We see the sunrise and sunset because of Earth's rotation about its own axis. Earth is rotating about its own axis from West to East. So, when seen from the Earth, the Sun appears to rise in the East and set in the West. Every day, the Sun, Moon, planets, and stars appear to rise in the east and set in the west. Actually, these celestial objects aren't moving that fast, but Earth is. It spins on its axis from west to east approximately every 24 hours. The sun itself also rotates in a counterclockwise direction. The satellites of the planets also generally revolve and rotate in a counterclockwise direction. Of the thirty something satellites only six do not do so; they are said to have retrograde motion.We do not feel any of this motion because these speeds are constant. The spinning and orbital speeds of Earth stay the same so we do not feel any acceleration or deceleration. You can only feel motion if your speed changes. During the short winter days the Sun does not raise exactly in the east, but instead rises just south of east and it sets south of west. Each day after the winter solstice, which occurs on December 21st, the Sun's path becomes a little higher in the southern sky. The Sun appears to be in constant motion rising on one side of the sky, moving across the sky, and setting on the opposite side. This apparent motion across the sky is due to the rotation of Earth. The sun warms up parts of the oceans. Warm waters rise just like warm air rises. So, as the warmer ocean waters begin to rise in a particular area, the cooler ocean waters from a different area will move in to replace the warmer ocean waters, and this creates our ocean currents. The Sun's energy warms the planet's surface, powering titanic transfers of heat and pressure in weather patterns and ocean currents. The resulting air currents drive wind turbines. When the molecules are heated, they move faster and move apart, causing them to be less dense and rise. When the warm air rises and the cool air sinks, convection currents are created. Surface currents in the ocean are driven by global wind systems that are fueled by energy from the Sun. Patterns of surface currents are determined by wind direction, Coriolis forces from the Earth's rotation, and the position of landforms that interact with the currents. While winds are responsible for ocean currents, the sun is the initial energy source of the currents. Since the sun heats the Earth more in some places than in others, convection currents are formed, which cause winds to blow. Large-scale, surface ocean currents are driven by global wind systems that are fueled by energy from the sun. These currents transfer heat from the tropics to the Polar Regions, influencing local and global climate.