If it’s in auto mode, your camera/video recorder will continuously adjust brightness based on the amount of light that’s available, so you can’t rely on it to do a test like this.
If you have a fully manual camera, you could set it to the exact same shutter speed, aperture, and ISO level, and then take two pictures - one at the beginning and one at the end of the test. Even then, it may have difficulty capturing super bright objects.
If you have an Android smartphone, you could try using the ceilingbounce app in a shoebox:
Otherwise, just get a light meter. To the naked eye, there isn’t a ton of difference between 6200 and 4000 lumen.