What does the tax office look at to decide whether I really left?

At the actual circumstances, not at declarations. Sections 8 and 9 of the Fiscal Code ask whether a dwelling is kept and where a person stays other than temporarily. That becomes verifiable through circumstances that leave traces anyway: whether the German home has been given up or let long-term, where the tenancy agreement and registration certificate were issued, where electricity and water are consumed, where accounts are held and cards are used, where children go to school, where the car is registered. The sum decides, not any single document. Anyone planning a departure collects this evidence from the outset. General information, not tax advice.