While driving, my turn signals stopped working.
I pushed the hazard lights (work fine) a few times, but still, not working.
Opened the service panel and checked Fuse 6, Yip : dead
Installed a new fuse, tried the signals without a running engine and they work fine.
But from the moment I start, the fuse dies again
Not familiar with the S2 wiring layout, but you may want to check each of the indicators including the repeaters for water ingress or corrosion.
On the S1 the indicators work on the ignition circuit and the hazard warning signals work from the battery circuit, both have individual fuses. Not sure why your indicators would work without the ignition on.