The Signal messenger and protocol.

I’m not too bothered about what is being sent with user consent

For an app to be private, it shouldn't be about "consent", but it should be about "demand". Send something only if the user demands it, not if they agreed to it. This goes with the principle of least surprise and the idea that the app should only act for the interest of the user.

the constant sending of identifiable and locatable data

Have you ever used such feature? I don't think you understand what is being asked. We're not talking about constant background location sharing (like I think snapchat is doing). We are talking about live location sharing with a contact or a group, for a limited period of time.

Here how it works in Facebook Messenger. The location is shared explicitly with a specific group of people for a limited time period, and the UI should make it pretty hard to forget, and deactivate automatically after a certain time.