Yes, I did unplug and replug the cable after reboot and found the respective lines in the log.
Today I also installed the newest merlin version which came out a few days ago. Maybe the issue is fixed in the new version, the red WAN LED didn't show up when I unplugged the cable before testing...
Thanks dave14305, seems to be working now with using services-start. I rebooted the router and Lynx's script was still active afterwards. I also ran the command "dos2unix /jffs/scripts/My_script.sh" on both files, just in case. dos2unix makes sure, that the script has some proper formatting...
Just replying to confirm, that this script is working and solved my issue with my Asus RT-AX68U showing a red light everytime my mobile network providers WAN IP lease would get renewed!
I am using a Huawei B818-263 LTE router and was running into this issue every few days. If anybody wants to...