Rub brisket on all sides with the BBQ seasoning, salt, and pepper.
Turn on the Instant Pot’s to the sauté setting. Let it heat until the setting indicates HOT.
Add the olive oil, wait 1 minute. Add the seasoned brisket into the pot. Using tongs to turn the brisket, sear on all sides until deep golden brown, 2 to 3 minutes per side.
Remove brisket. Add sliced shallot to the bottom of the pot. Return the brisket, fat side up, to the pot.
In a small bowl, whisk together the red wine, vinegar, ketchup, and water. Add the mixture, pouring it around into the inside perimeter of the pot. Cover, lock the lid, and make sure the valve is set to seal according to manufacturer’s instructions. Set to Manual, HIGH pressure, and enter 70 minutes on the timer.
When the brisket is finished cooking, let all the steam and pressure release naturally, 20 to 25 minutes. Then unlock and carefully remove the lid.
Remove the brisket to a cutting board, lightly tent it with foil, and let it rest for 10 minutes.
Meanwhile, pour the pan juices, including the shallots, into a medium, heavy bottomed saucepan. Bring to a boil over high heat, then reduce the heat to maintain a brisk simmer. Reduce the sauce by about one-third or until you have about 1¾ cups sauce, 12 to 15 minutes. Season to taste with salt and pepper.
Slice the brisket across the grain into 1/4-inch-thick slices. Serve with the reduced pan juices and shallots.