For those of you that do back-to-back batches on e-brew systems, do you clean your boil kettle/elements between batches, or just rinse them out and keep going?
Totally don't do any cleaning between brews. I just go to the next batch & hit it. I clean at the end but I'm also very much a "free spirit" brewer. I don't pay much attention to style & mainly do 13 gallon SMASH recipes that I make up on the spot. So if you are brewing a rather delicate style beer for your 2nd you may need a bit of cleaning if you just finished a fat stout or something. From my point of view & what I brew cleaning between doesn't make sense but for you it may.
I hose off the inside, especially the element, and then check it with my fingers to make sure there is no crusty buildup. I don't want to risk scorched wort.