There is a usual problem that causes this on Cessnas.

Cessna solid state voltage regulators on pre-1980 alternator equipped
Cessnas had three wires. One for the aircraft bus, one for the alternator
field and one for ground.

The alternator field is switched on and off rapidly by the reglator to
maintain 13.8 Volts or 27.6 Volts (depending on whether you 14 or 28 volts).
The regulators were made by Ford (I think). The regulators switch the field
on and off. They are not analog dvices.

THIS IS THE PROBLEM:

The "Aircraft bus" lead on the regulator serves both as the voltage sense
lead and as the power lead to ultimately provide power to the alternator
field. When energized, the field draws about 2 amps. If there is ANY
resistance in the path to the voltage regulator from the aircraft bus, you
set up a condition for oscillation. Just 0.2 ohms, for example, will cause
a drop of 0.4 volts in the sensed voltage when the alternator switches on.
When the field is switched on, the sensed voltage drops and when the field
is switched off, the voltage increases. This causes the alternator to
switch on and off at about 5 hertz and the bus voltage to oscillate up and
down by a volt or so. This causes the lights to flicker. Since the overall
sensed voltage is lower than bus voltage due to resistive drop, the battery
overcharges as well. An average overvoltage of .2 or .3 volts is a LOT when
charging a battery and it will boil it dry every 20 hours or so - a symptom
of this problem. The problem resistance is often in the contacts of the
master switch. They have to be meticulously cleaned. Even then, slight
oscillation occurs.

This is obviously a big design defect. In about 1980, Cessna apparently
realized this and changed to a voltage regulator with four leads, the extra
one being a separate "sense" lead connected directly to the aircraft bus so
that the alternator field did not draw current through it. Ironically, if
you open up an older regulator, there is a separate "sense" lead in the
circuit, only it is jumpered to the + lead internally!

Clean your master switch meticulously. There is an easy permanent solution
to this problem but it is not legal. Good luck.

DB