The FindMy app displays the current position of any AirTag that is linked to your account, however you can't monitor the journey of an AirTag over time. Besides that, an AirTag's location history is not stored within the tag itself. This is part of Apple's attempt to limit the usefulness of the AirTag as a stalking device, along with other security features that detect and notify you about nearby AirTags that are not yours unless their owner is also present. 

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How often does an AirTag update its location?

It all depends! AirTags do not immediately transmit their location to your phone. They instead send their location data to surrounding iPhones or other devices in Apple's Find My network. These gadgets then send that information to you automatically and securely.
If your AirTag is in a crowded area with a high volume of iPhones arriving and departing, its position may be updated every minute or two. However, if your AirTag is in a really remote place, you may cease receiving location updates entirely since the AirTag physically cannot reach you if there are no other Find My devices within its radius.

How do I stop sharing my location on AirTag?

• In iOS 13 or iPadOS 14 or later go to Settings > Account Name > Find My > Find My iPhone/iPad, and disable Find My network.

• In macOS 10.15 Catalina or later, go to the Apple ID preference pane, select the iCloud link at left, click the Options button to the right of the Find My Mac item, and uncheck Offline Finding or Find My network (the text varies by macOS version).