Flight Instructor reported a misunderstanding of the ammeter readings led to an electrical failure in flight; a manual gear extension; and the inability to communicate with ATC at a towered airport.

Narrative

During preflight with my student; I noticed that there was a slight trickle of water coming from the magneto switches in the cockpit. I was surprised; but not alarmed - I thought I would attempt to start the engines and that if anything was truly amiss then a circuit breaker would pop. None did; and the airplane started fine. All electronics seemed to operate normally.During alternator testing; I noticed that the ammeters were not reading properly. Shutting off the master switch did not shut down the electrical system; so I believed the alternators to be working. I tested the system using each alternator by itself with the master switch off and the electrical system functioned properly with the exception of the ammeter gauges - sometimes they read charging; sometimes they read zero. I did not receive a low voltage light warning on either alternator. Since the electrical system stayed running with either of the alternator switches on; I believed that they were both working and that the gauges themselves might be faulty. After approximately 75 minutes of flight; I instructed my student to land at ZZZ1. The ammeter needles had read zero the entire flight; so I thought I should test the system again. Shutting off the master switch (on the ground) resulted in a complete electrical shutdown. At this time; I thought the alternators were working intermittently; as I did not believe we had been flying with full electronics on for over an hour on just the battery alone. I turned the master back on; and we flew back to ZZZ. Enroute; the NAV2 circuit breaker popped; and I chose not to push it back in as I did not know what was causing the electrical problem. I still had full use of my COM1 radio; a Garmin GTN750. As we neared ZZZ and contacted the tower; I noted that the screen on the GPS was beginning to flicker. I notified the tower that I was about to lose all electrical power. Tower gave me a lower altitude and said they would call my base turn. At that point; I lost all electrical power and could no longer communicate. I attempted to lower my landing gear; but did not have sufficient power to do so. I guided my student through a manual gear deployment and advised him that this would have to be a no-flap landing. I tried to contact tower; hoping that my transmission would get through - the screen on the 750 was still flickering off and on. I could hear tower attempting to call me; but I did not have sufficient power to transmit. They did not respond to my radio traffic. I performed a no flap landing and exited the runway when I saw that it was safe to do so - I then ensured that the taxiway was clear and taxied back to my parking area; still unable to use my radios or any other equipment. In retrospect; I could have not taken off in the first place; since the gauges were not operating correctly. I also could have stayed on the ground at ZZZ1 once I discovered that we were essentially running on battery power alone. I also could have notified Approach as to my predicament prior to arriving in ZZZ airspace.