What do I do when two squares are equally valid?

There is no way to logically determine which square to pick here

I'm afraid there's no special trick or anything to solve this situation reliably. All the available information is clearly displayed for you, and there's an equal chance of either square having the mine. Minesweeper simply isn't designed to be logically solvable 100% of the time. This is why sides and corners are somewhat dangerous, though the situation can happen in other ways, too.

All you can do is guess and hope for the best.

Logically, no

Either of those squares can contain a mine, as you have noted. So there is no way to determine which one.

Statistically, maybe

Because the last mine left is either in the upper-left corner or the square to its right, an answer to another Mine Sweeper question may help a bit, though.

If a mine is under the first clicked tile, it is moved to the upper-left corner, if the upper left corner is occupied, the mine moves to the right of the corner tile.

That is sourced to someone who reverse engineered the game.

Statistical analysis

So if you happened to have landed on a mine on your first click, that mine has been moved to the upper-left corner. It can't have been moved to the square to its right, since that would mean the upper-left corner was already occupied by a mine, but there's only one mine left in your example.

So if you did not land on a mine on your first click, you have a 50% chance for either square to contain a mine. If you did land on a mine on your first click, the mine will be in the upper-left corner. Since your board has 99 mines on a 16×30 grid, there's a 99 in 480 chance of having done so.

Combining these, you have about a 60% chance of the mine being in the upper-left corner and a 40% chance of it being in the square next to it.