In endgame, what is your top priority besides defending the king and checkmating the other?

My personal top priority at that point is pawn promotion. Easier Checkmate.

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My endgame priority is to make the opponent run out of time if it's blitz or bullet lol.

For longer timed games my priority besides checkmating is to make the opponent blunder or stalemate.

I'm not the best, but my goal in endgame is usually to just eliminate all the opponents pieces while not losing any of my own pieces.

This question is too broad.

"...to crush your enemies, see them driven before you, and to hear the lamentations of their women...!"

Well, some general ideas are to take your time because mistakes in the endgame are especially deadly, have active pieces (including your king), and try to prevent your opponent activating his pieces.

I 've written an article that shows all of this and a bit more in depth. This might be of use to you:

https://www.chess.com/blog/nklristic/how-to-approach-the-endgame-first-steps-to-chess-improvement

Have in mind that all of us weaker players are not particularly good at the endgame play, but by doing above things (and other described in the article), you will be less bad and certainly better than your current peers.

Thanks for the advice!

Avoid or pursue stalemate,  use bishops to trap knights if necessary and evolving de pawns to threat a promotion.

Reduce the opponent's options while retaining as many of yours as you reasonably can.

Also.

Be aware of when rules of thumb lead you wrong.  Watch for when having a knight is better than a bishop even with pawns on both sides of the board.  Watch for when going into a K+B+pawns vs K+B+pawns ending is winning even with the bishops traveling opposite colored squares.  Watch for when "blundering" a piece can draw your opponent out of position and allow queening a pawn.  Watch for when allowing your opponent a protected passed pawn is a draw (example White Kb2, Pa3, Black Kc4, Pb3, Pa4 - as long as the White king is in the a1/a2/b2/b1 square the only progress Black can make is stalemate) and it can sometimes even be a potential win.  Any time you see something like that there is a decent chance that the opponent will follow conventional wisdom and play suboptimal moves.  Note - Don't make weakening moves trying for such trickery unless you are already losing (or unless there is a fall-back draw and you are not otherwise winning).

I try to trade my pieces favorably.

King activity.  Most endgames come down to this.  Once the heavy pieces are off (and really even if your opponent still has a rook left), the king needs to move into the attack.  Leaving your king in the corner is often worse than being a piece down.

Create a passed pawn and promotion threats. Centralize the king and bring it into the game. Limit your opponent's options as much as possible. Try to make accurate moves and keep the pressure up.