Starter Relay - What am I missing???

The meter will not put a "load" on the ground connection. Like others have said here if you have on strand connecting the brown wire to ground then it will measure battery voltage. The real test is using a device that will draw current though that ground connection (headlight). Connect from battery positive to the brown wire and see if it lights. If not then check the wire AND don't forget that the neutral safety switch itself might be bad.