Hi Rob,
I think this should work fairly well with a Mendix Native app. I think from an implementation point of view you want to implement this in Javascript actions as this gives more control on your navigation flow and will therefor make it easier to send custom events to Google Tag Manager.
Depending on the platforms you will support it will be necessary to create a custom Native app instead of using app center. You will need to install the Node dependencies in you javascriptsource folder with the npm install/yard add command. After you should be able to use the library straight away in JS actions on Android. If you need to support iOS you’ll need to make a custom developer app to test your local Mendix instance and a custom production build for App Store releases.
Working with Custom Native apps means cloning the Native project from the Github repository and open this with XCode and/or Android Studio. The process for this is explained in the following doc: https://docs.mendix.com/howto/mobile/how-to-devapps#4-installing-your-custom-developer-app-manually
you can use the same steps for the custom production build.
Please take a look : https://github.com/rangle/redux-beacon/blob/master/docs/targets/google-tag-manager.md#setup