If you are not making calls, sending or receiving texts and not using your mobile data, your phone is in the so-called "idle state". No minute-by-minute history of your cell position is then created by your provider. The wireless network is then only aware of the last so-called tracking area or wireless cell. This is a network of a large number of radio towers that does not provide a reliable indication of your exact location. However, if you are on the phone or your internet connection is continuously active, these tracking area updates (TAU) happen much more frequently. The movement profile of your device is therefore much more accurate. These records are linked to your name through the registration of your SIM card and can be requested by authorities such as the police.
Keep in mind that turning off your mobile data will only reduce the frequency of updates. Your phone will automatically report to the wireless network at periodic intervals even when idle. In most cases, you cannot influence this. The hardware of your device does this automatically and you have no control over it. If you really don't want to be found, remove the SIM card, switch your device to flight mode or use pseudonymous SIM cards.
Also bear in mind that apps and their providers can track you less easily using your IP or your location if you don't have your mobile data activated at all times.