Your urine isn't going to show acetoacetate unless you're in ketosis. You're not supposed to use ketones to test accurate levels. It's to give you an idea of what's going on. There's no way your strips are going to show purple if your body isn't producing ketones for energy transport. The exact level doesn't even matter that much because what shows up in the urine is
excess. Sure, acetoacetate is not the only ketone, but it doesn't just get created within the body for no reason. If you are fasted and you eat a bunch of ice cream, your ketone strip test will plummet to showing no signs of ketones at all. If you are fasted and you eat a fatty steak, at best you might see a slight decrease because of protein intake. This is consistent and easy to reproduce. I've repeated this test
dozens of times. Carb and sugar heavy food plummets urine ketone levels and keto macros don't. Your body isn't going to produce an appreciable level of ketones when it's got simple carbs ready to go, which is because the body is going to prefer glucose every time it's given a choice.
And yes, you do bounce in and out of ketosis when you fast long enough, and it really doesn't take that long. Once you've expended your glycogen and you've digested all your food, your body doesn't have a choice but to dig in to fat stores. Depending on how much glycogen you have stored, what you've eaten, and how long it's been since you've eaten, getting into ketosis becomes ridiculously easy because the energy your body uses has to come from somewhere. You don't need to measure ketones to have confidence in this. It's well studied. If someone thinks that ketosis is hard to enter, I doubt they've gone more than a day without food. Once you get used to fasting for longer than 48 hours, it becomes obvious when your body is out of glycogen.