I have a 2016 Haval H2. Have any of you experienced a brake light fault warning when pressing the brake pedal for a long time, but the warning disappears once you restart and press the brake again?

The brake light is out, replace it yourself.

Find someone to help you press the brake pedal, then check which brake light bulb is out. You can buy a bulb online for 5 dollars. Get a socket wrench, remove two screws, and you can take the entire tail light out to replace the bulb.