The one side with fast action sound looks normal on the gauge however, the side that deflects the amp gauge ( alt gauge ) to almost maximum discharge current draw is indicating a huge not normal current draw. But you know that... You could have one of a single or multiple issues... could be a lamp that has an internal short, a wire associated with tail lights / turn signals that is shorting to chassis or pinched somewhere. I'm suprised that this condition has not blown a fuse. I would certainly not leave the bad side active for more than a split second, otherwise you are going to have a major meltdown or possible fire at that current draw amount !!
I would start by removing all lamps on the bad side front, rear, sides basically anything that's associated with turn signals and see if problem clears. If not, you got a wiring problem or possible issue in turn signal switch or wiring in steering column. My 2 cents worth...