The oozing is the obvious problem. Having the temperature too high during homing (wrong filament selected) or wet filament (moisture turns into steam and “pops” more filament out). The major flaw of the Taz 6 is reliance on the electrical connection with a nozzle that’s almost always partially covered in an insulating material.
The way it detects is to get the very rough zero from the button press. That rough zero lets it set the maximum the machine will move down when checking the washers.
From there it goes to the first washer. When zeroing on a washer it will move down until connectivity is registered for the initial zero (or it goes below the maximum detection depth and fails). If it succeeds in getting a measurement for the initial zero, it lifts off the washer before lowering at a reduced speed to get actual zero. After getting that second electrical contact, it will slowly lift (the ticking you hear) until electrical contact is broken. The height that electrical connection was last detected is saved as the zero height for that corner. Rule of thumb, if it ticks more than six times when lifting, it had to push too hard, and your nozzle is dirty.
If it fails to get connectivity before the maximum depth, it will halt the printer. If it gets connectivity too soon, it will halt the printer.
After the first corner is measured, it moves to the second. At this point, there is much less deviation from the zero position accepted (something like 1-2mm, depending on firmware version). Any amount of plastic on the nozzle can electrically insulate the nozzle from the washer. A .01mm thick insulator is still an insulator, and it may require pressing the nozzle down pretty firmly before connectivity is achieved. The rule is that if you visibly see the washer get pressed down AT ALL the measurement is off, and even if bed leveling succeeds, your measurement is off, and failure is likely.
So, in the video, you get the first measurement (nozzle 1 looks fairly clean), but nozzle 2 is visibly oozing the entire time. It usually fails on that second one because it goes down beyond the maximum. It did get a measurement on #2, but not on #3 within the allowable margin and halted.
Additionally, your X axis gantry may not be parallel to the bed, judging strictly on how long it took to lower the nozzle. Hard to tell from the video though, but that can also contribute to failed leveling.