They dont need to know / proof s**t. They will simply send you the tax bill with a 14 days payment notice, estimate or right away charge you with tax fraud. YOU have to proof it and they are the ones deciding if your proof is plausible enough. Usually that will also mean you have to pay first before that all goes to court.
Tax law is guilty until proven innocent not the other way round.
And no tax law and double tax agreements in most countries do not specifically declare what "center of life" is. This is pretty much at the mercy of the︀ financial court judge / your home countries tax agency and you can only use previous︁ rulings as a guideline.
In general as long as you have severed ties, are out︂ of the country 183+days, no car registration, no real estate, no company shares, no marriage,︃ no apartment, majority of your funds outside of your old country, etc pp and got︄ proper residency + tax residency permits + certificates in our new country, stay there LONGER︅ than you stay in your home country (e.g. 120 days in germany and only 60︆ days in cyprus, rest scattered around the world is not going to cut it even︇ if fine with the basic law) and can show flights + bills etc you will︈ usually be fine. In some cases however they go much further with things like how︉ is your social life in the new country, doctors, hair dresser, etc pp.