If you are not making calls, sending or receiving text messages 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 any reliable information about your exact location. However, if you are on the phone or your internet connection is constantly 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 person through the registration of your SIM card and can be requested by authorities such as the police.
Bear in mind that switching off your mobile data only reduces 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.