Flickering and surging at two campgrounds followed by no flickering. Plugged into 30 amp shore power...
Flickering lights and surging furnace fan indicates a 12 volt issue. Both items operate on 12 volts.
Running on shore power means converter is supplying 12 volt power.
Possibly there is a faulty converter.
Possibly there is a loose 12 volt positive connection.
Possibly there is a loose 12 volt ground connection.
Do the surging and flickering happen at the same time?
Did lights flicker when furnace fan was not running?
Air conditioner running fine means no 120 volt AC issue.
No problem with lights at third campground when furnace is not running? It still could be a loose connection.
Check for loose connections at battery, converter, and anything in-between. Check both ground and positive cables. Check main converter fuses for secure insertion and signs of heat. Visually search for corrosion and discolored or melted insulation near connections.
Reset converter 120 volt breaker by turning it off then on again. Switch off main breaker and check converter 120 volt breaker wire connections.
I wish you good luck and happy trails ahead.!