Sounds like your 'converter' is failing.
When connected to shore power the converter takes AC power IN and puts DC power out.
That DC power is used to supply all dc demands and recharge the battery
Converter DC Voltage output should be steady (depending on demand).
When converter starts failing the DC Voltage will fluctuate.
AND this dimming/brightening of lights can be due to a bad battery......shorted/bad cell
So you need to check each battery cell 'specific gravity', check battery voltage/load test and converter DC output with battery disconnected....voltage S/B 13.2V
Time to buy a digital volt meter and learn to use one......every RV owner should have one and know how to use it.