About Theta Z1 some questions

Is there a way for theta Z1 to synchronize the Linux clocks?
Is there a way for theta Z1 to customize the name of the photo file when the photo is stored?
Is there a way for theta Z1 to set the camera storage media somewhere natively in Linux?

The camera runs an internal version of Android version 7. Using a plug-in, you can set the time of the camera. However, this may not be the synchronization that you are looking for. You can’t synchronize two camera effectively. There are same tests using a flash or a timer to match the frames of two cameras in post-shoot, but not during the shoot.

If you are taking still images.

Date_time_zone

You can set custom names with the plug-in.

You can set the storage media with the plug-in.

Example, old, but you can see the concept.

Concept Ideas - THETA V Plugin Development Community Guide

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Feel free ask more questions and share more of your use case. If you share what you are trying to do, we may be able to provide better ideas to try and answer your questions.