Like you said:

~$ df -k /var/run
Filesystem     1K-blocks  Used Available Use% Mounted on tmpfs               # tmpfs
806412   832    805580   1% /run
~$ 

~$ ls -lid /var/run
913937 lrwxrwxrwx 1 root root 4 May 21  2017 /var/run -> /run                # symlink
~$ 

~$ lsattr /etc/resolv.conf
lsattr: Operation not supported While reading flags on /etc/resolv.conf      # same error with [chattr +i]
~$ 

~$ lsattr /var/run/connman/resolv.conf
---------------------- /var/run/connman/resolv.conf
~$ 

~$ lsattr /run/connman/resolv.conf
---------------------- /run/connman/resolv.conf
~$ 

Like I said before, with respect to connman and what it does with /etc/resolv.conf:

Thanks for your input.

Best,

A.

That would explain why chattr -i didn't seem to work. Checking with lsattr might be interesting too.

No, not that.

Turns out that NetworkManager at some time in the distant past, left a few remnants.
It was not installed and hence not running. See post #1.

Well ...

That is the mystery still afoot.
Since my last post, my box has been rebooted no less that 3 / 4 times a day for the last week or so.
And for all those reboots and time it was on-line (up to seven hours a day) connman has (knock wood) seen it fit to leave my /etc/resolv.conf alone. 

But here's the thing®: I have no idea why.
ie: attempting to apply +i chattr to /etc/resolv.conf, tis last file being a symlink to /var/run/connman//etc/resolv.conf only gets an error message.
So I don't think what seemed to be the accepted solution took hold.

Hmm ...
systemctl?  -> surely you jest ...

Thanks for your input.

Best,

A.

:-)

wicd is back from the dead

FWIW, I am also a wired user but still miss wicd.

Getting back on track as per my OP.

1.
any NetworkManager files present in my system while that package was not installed can only be adscribed to remnants from either Jesse or ascii - cannot come up with any other explanation.

2.
evidently both NetworkManager and connman take the liberty of screwing around with /etc/resolv.conf which explains the banner left behind by the first.

With respect to whatever/however it is that connman screws around with /etc/resolv.conf, I have not been able to find a clear answer.
Yes, it does edit/replace the file but when and why is still a mystery.

To wit:
Applying chattr +i as sudo/root did not work and connman kept on changing my local DNS setting for my FO provider's.
This in spite of the local DNS address being set both in the FO provider's router and in the connman settings page.

And then, all of a sudden ...
... It has stopped doing it.

Why?
No idea.
Maybe it has a mind of its own?  8^°

The thing is that my local DNS setting has remained as required by me for ~ 48 hours and survived at least a half dozen reboots.
If it acts up again, I will just nuke the symlink and reinstate /etc/resolv.conf as a text file. 

But still ...
I am not at all happy with not knowing what is going and exactly why.
Much less with applying brute force (chattr +i) to keep it from happening.

So I am planning to approach the solution suggested by Ralph.Ronnquist: use ifupdown.

I found an interesting page with what seem to be a set of comprehensive instructions to make the conversion to ifupdown.

But I'll have to study them before taking any action but I think it is definitely a step in the right direction.

Thank you very much to all those who pitched in.
Marking this one solved.

Best,

A.

When you say "no network manager at all" you actually mean "just using ifupdown".

... Whatever got installed with cinnamon with --no-install-recommends, no additional packages.

I see ...

When I left a shared WiFi arrangement to get an ADSL and then went on to fibre, I kept WiCD and a network management application (whatever came with Daedalus as default when I upgraded from Beowulf/Chimaera) just to be able to use a wifi spot nearby, just in case fibre goes down.

But 99% of the time I am using LAN, just like you.
Maybe I should look into doing just that ...  8^°

If you could share your how-to I'd be very obliged.

Thanks in advance.

Best,

A.