How do I detect camera movement?

There is no camera moved event but you can use the changed event since the CFame is the camera position.

This is a local script:-

local cam = game.Workspace.Camera

cam.Changed:connect(function(propString)
    if propString == 'CFrame' then -- only look for the CFrame changed 
        print('Camera Moved', cam.CFrame)
    end
end)

There are other ways of doing this, but this uses the existing events that Roblox provides.

Hope this helps.