Diagnosis
That rhythmic clicking is completely normal and is the sound of the auger feeding pellets. It's not a problem, but it can be surprisingly loud on the Tailgater because the whole unit is more compact.
How to Fix It
There's no 'fix' because it's not broken. The auger is a corkscrew-like rod that turns in short bursts to push pellets from the hopper into the firepot. That 'click... whirr... click' is the electric motor engaging and disengaging. To confirm this is what you're hearing, stand next to the grill and watch the hopper when you hear the click. You'll likely see the pile of pellets shift slightly as the auger turns.
If That Didn't Work
If the sound is more of a constant grinding or a loud screech, that's different. A constant grind could mean the auger motor is struggling because of a jam. A screech might be a dry bearing. For a suspected jam, you'd need to power down, cool, and vacuum out the auger tube from the hopper end (using a flexible hose) to clear any damp, swollen pellets.
Heads Up
If you ever stop hearing that click entirely during a cook, that's a bigger concern. No clicking means the auger isn't feeding, and your fire will go out. Check for a jammed auger or a tripped GFCI outlet on your power source first.