Imagine:

The magician introduces a deck of cards. The spectator can thoroughly examine it, after which they can freely shuffle it for as long as they want in any way that they want. Once they're done shuffling, the magician invites them to spread through the deck face down and select any two cards that they like. They leave these face down on the table. The magician then instructs them to turn one of them face-up - let's suppose it is the JS. As for the other one, the magician tells the spectator not to look at this card yet - it will be a mystery for the end.

The spectator is then asked to place the unknown card face down on top of the face-up JS. With that done, the magician tells them to bury the pair anywhere inside the deck - the magician looks away as they do so. Finally, they are asked to give the deck as many complete cuts as they want so even they don't know where the pair ends up.

After all that, the magician turns back around, takes the deck from the spectator, and immediately brings it behind his back. (Alternatively, the spectator can place the deck behind the magician's back into his hands while he's still looking away.) Whilst holding the deck behind his back, the magician explains that he has an uncanny ability where he can find face-up cards without being able to see any of the cards. He explains that he will find the unknown selection by feeling for where the face-up card is. Furthermore, the magician explains that he has a second uncanny ability where just by touching a card he can reveal what it is.

The magician claims that he's found the unknown card and is touching it, and slowly begins to reveal its color, its suit, and finally its value. He claims it's the 6H (for example).

Finally, the magician brings out the deck and hands it to the spectator. They spread through the deck to find the face-up JS, after which they turn over the card above it (the unknown selection). It is indeed the 6H.

Some important conditions of note:

The deck can be completely examined by the spectator at the beginning - it is ungaffed / ungimmicked in every way. It's just a regular deck. The spectator can also examine the deck at the end if they wish.

From the moment the spectator shuffles the deck to the moment they lose the pair inside the deck, the magician doesn't touch the cards. He especially doesn't touch the selections.

This method works even if all the cards in the deck are perfectly straight (without any natural bends) - this is to rule out one possible method that some people may have thought of when reading the description above.