I never trust the tweeter wands.
A multimeter goes a long way in troubleshooting these things
Based on your description it sounds like you are using a 3 prong plug-in style tester with 3 LED indicators side by side. Those testers are good for a quick polarity check and testing grounds, but are not of much use when it comes to troubleshooting. If you have a regular digital voltage tester then run tests for voltage from hot to neutral (should be ~110VAC), hot to ground (should be ~110VAC), neutral to ground (should be ~0VAC), continuity between neutral and ground (should be low/no resistance with the breaker off for any continuity tests), continuity between hot and ground and hot and neutral (should be open circuit or very high resistance with the breaker off for continuity tests).
If this testing shows no continuity between the ground and neutral then the neutral connection in the receptacle may be open, the connection between the neutral wire and the neutral bus in the panel may be loose or a connection may be loose somewhere between the panel and this receptacle.
Also check the neutral on another circuit or two. If that is open too then the neutral bus may have come loose in the panel. Check that out and remove, clean and retighten the connections. If there is corrosion in the breaker box then you may need to disconnect, clean and reconnect all the connections (hot, neutral and ground) to avoid intermittent issues on other circuits as well.
If that doesn't fix it then there could also be a receptacle outlet, light switch, or a junction box between the panel and this receptacle and a loose neutral connection could be there.
Trace the circuit back to the breaker panel and check the neutral. If you find a point in the circuit where the neutral is connected then you can start working between there and the end of the line to find the open connection.
If you don't have a good neutral somewhere else along the circuit, but the neutral is connected to the bus in the panel then you will need to check and tighten the neutral connections.
Make sure the circuit breaker is off when you do this. Check/tighten the connections to the neutral bus bar in the breaker box and work your way back out to the end of the line tightening the connections as you go.
Just as a cya statement, I AM NOT A PROFESSIONAL ELECTRICIAN, do this at your own risk
