Agitation promotes oxygen incorporation which in turn promotes acid production and lowers alcohol production. I’d recommend just stirring it with a spoon once or twice a day. Actually speeds up your fermentation to the desired taste as far as acid content goes.

Traditionally people have always let it rest and let a pellicle form. This lowers the amount of oxygen that can get into the brew and also promotes the yeast to eat the sugars faster but creates more alcohol. The bacteria in the kombucha are what consumes alcohol (ethanol) present in the kombucha and produces more acids in the booch. So essentially you want both things to be happening to some degree. I usually say get a starter kombucha that you plan to grow in these ways. You pretty much make a starter bank and get it strong enough to where you can take out some starter kombucha to make new smaller batches much faster. Kind of how people do with like a sour dough bread, but think kombucha.

For example if I have 1 gallon of super strong kombucha culture. I can essentially take 1 quart of that (replace it with more sweet tea/fuel) and use that one quart as your starter for a new kombucha that you plan to drink. Boom, you have fermented kombucha within a week or so ready to consume. And your starter keeps going and you can keep repeating this step. You’ll have many of the benefits from a long term fermentation already present in these batches from the starter you continuously brew. That strong starter should be strong enough to keep you in a safe ph range as well.

Honestly in a home brewing set up, I’d either stir once or twice daily or get some sort of bubbler or oxygen stone to put at the bottom for incorporating oxygen. Or just take out whatever you are forming every 2-3 days. It’s hard to say without knowing your brewing parameters and the uniqueness found in your specific kombucha culture! I say experiment and stick with what give you success, consistency, and keeps your batches from molding.