An instructor pilot reported engine malfunction on initial climb and return to the airport.

Narrative

The first indication of a problem; I was 8 Miles away from ZZZ; and my low-voltage light illuminated. I took little to no credit in it being a real issue because it would come in and out during previous flights. I was told this was a common issue with that type of sensor but it was not an actual low voltage scenario. I checked the voltage; that along with other things gave me no other indications of an actual low-voltage scenario. I then did 4 landing's to hit the PPL requirements for my student. On the downwind of the last landing the panel light; out of nowhere doubled the level of illumination. This put me in an on edge mindset but ended up not factoring into the mechanical issues moving forward. We did our final full stop taxi back and took off on XX and departed straight out to the south; at about 4;000 feet and 4 ish miles south of the airport. The engine cut out for what felt like 2-3 seconds. I immediately took control of the aircraft from my student and immediately started a turn back for the airport. Before the 180-degree turn was complete the engine was back to normal as it seemed. I quickly advised ATC for a few reasons; One was that I knew from my weather briefing that XXX.X would not be unavailable in the area of this airport; Two was that I was not on flight following nor did I file a VFR flight plan. With the terrain in the area; it being night time; and no one knew I was out there I was worried that if the problem got worse which I was expecting it to I would either not have the time to get my distress out; or the line of sight; and with my already on edge brain and the sudden and significant loss of power that understandably put me in emergency mode a lot quicker than it needed to be. I had plenty of time and altitude looking back and I should have given myself more time to fully take a breath and evaluate the situation once I was heading back in the direction of the airport. I then advised an airliner above me and he transferred the message to ATC for me. I made minimal power adjustments because I was on edge that any big or sudden changes in power could kill the engine completely. I made the landing with no further issues. I ran the plane up on the ramp to get a better understanding of what happened in a safe and controlled environment and detected a 1;000 RPM drop on my left magneto. I shut the plane down and called it a day. The reason for the sudden and abrupt power loss followed by an engine returning to what seemed normal was caused by two main factors in not only in my own; but also the mechanics opinion on the situation. The first was corrosion in the magneto wiring; and the second was fouled spark plugs from the fact that I was full rich mixture per the POH; and was for about the next 30 minutes doing full stop taxi backs on full rich the entire time.