C172 instructor pilot with student reported fuel indication issues during cruise flight resulting in a diversion. Reportedly; the cause of the issue was a faulty wire for the analog gauges.

Narrative

During Cruise Flight; Student noticed Fuel Quantity Indicators were indicating 0 Fuel on both left and right tanks. We notified ATC that we would like Divert to ZZZ (nearest airport) due to our fuel indicators showing 0 Fuel. Approach responded with 'I understand you're [requested priority handling]' and since we were unsure if the indication was accurate we agreed to the said statement. We continued to have normal operating parameters with regards to engine power and flight controls and weather conditions so we descended down and complied with ATC instructions. We got switched over to ZZZ Tower in which we performed S-Turns to final. Upon landing; our fuel indicators were working properly. We called the owner of the flight school and communicated with the mechanic and they told us that was a faulty wire for the analog fuel gauges; that if it happened again; to cycle the master. The fuel on board the airplane was more than adequate and the gauges were working properly so we proceeded to fly it back to ZZZ1 Airport.