mh,
at the moment i have no time to test this.
Do you use systemd as init system?
If you dont know, or wait, provide us the output of
inxi -xI
If you use systemd, you can search for ifup@eth0.service and ifup@wlan0.service.
First in grafical.target (init5) then after switching to multi-user.target (init 3), then after ifup eth0 (in init 3).
good luck
edit: do you use NM for to connect to the world?
Or, how did you set up your network?
edit part 2:
First: an ifup@eth0.service does not exist on my system, so i gues also not on yours!
An ifup@wlan0.service exist, this could be a left over.
When i had the same trouble with wlan0 i wrote myself an ifup@wlan0.service, because i was tiered about
to type every time ifup wlan0 when switching to rl 3.
Well, ok, i have tested it, wlan0 down, eth0 up, switched to multi-user.target (init 3), eth0 still working.
So we need more informations from you.
We lost our world wide funtional crystal ball, so i/we can't debug your problem.
btw. i do not use NM.