What was this beacon-like light in the distance that disappeared?

The other day I noticed a yellowish/white beacon-type of light (unfortunately, I forgot to take a screenshot), really thin and stretching to the sky, on the side of a mountain — just north of Hateno Village. I went in that direction, but unfortunately didn't get there before it disappeared, and didn't find anything in the location. This was not a beacon I placed with the scope or in the map directly, just to clarify.

Maybe a different thing, but I also saw a glow near Satori Mountain, but that looked kinda different — it was wider (not a "beacon") and blue. As I approached this one also seemed to not be visible any more (ended up finding a temple there, but since I saw the glow for very far away, it seems odd that the glow was there to mark this temple...).

What were these lights? Were they one-off things tied to these locations that I missed altogether? Or are they something that happens every once in a while in various places?

I noticed a yellowish/white beacon-type of light

This was more than likely a Shooting Star. A Shooting Star is an over-world event that provides Link with various treasure when you find it. The treasure varies depending on the color of the beacon. With it being a yellowish color, it would have provided a Star Fragment; a material to upgrade your armor.

If you have the DLC and started the quest Xenoblade Chronicles 2 side quest, a shooting star with redish light will start appearing

I also saw a glow near Satori Mountain

This means the Lord of the Mountain has made an appearance at the top of Satori Mountain.

There is a lot of lore surrounding this being. As for game play purposes, the Lord of the Mountain can be used as a mount, but it cannot be registered at the stable. When mounted, it has max speed and strength and practially never runs out of stamina