Ok, your Codec looks good. Here's the pin node of your headphone:
Node 0x21 [Pin Complex] wcaps 0x40058d: Stereo Amp-Out
Control: name="Headphone Playback Switch", index=0, device=0
ControlAmp: chs=3, dir=Out, idx=0, ofs=0
Amp-Out caps: ofs=0x00, nsteps=0x00, stepsize=0x00, mute=1
Amp-Out vals: [0x80 0x80]
Pincap 0x0001001c: OUT HP EAPD Detect
EAPD 0x2: EAPD
Pin Default 0x04211020: [Jack] HP Out at Ext Right
Conn = 1/8, Color = Black
DefAssociation = 0x2, Sequence = 0x0
Pin-ctls: 0xc0: OUT HP
Unsolicited: tag=01, enabled=1
Power states: D0 D1 D2 D3 EPSS
Power: setting=D3, actual=D3
That says you have an ALSA control "Headphone Playback Switch", which is currently muted. Unmute it in
alsamixer (press right arrow until you see it, select it, press m), and you should hear something, or at least get an additional port in
pavucontrol that you can select to hear something. It also says that it can detect plug events, and currently it's plugged in. To verify that the detection work, run
evtest as root, pick the one that looks most similar to "HDA Intel PCH Headphone", and remove/plug in the headphone. You should see the events.
If unmuting the Headphone Playback Switch control doesn't work, please add the output of
amixer -c0 contents to the pastebin. One possible complication is that the headphone has an external amplifier ("EAPD"), and that is sometimes controlled by the BIOS or SMM firmware.
Edit: Ok, next step is to make sure the external amplifiers don't interfere. There are cases when the external amplifiers don't come up after hibernation etc. So completely cold boot your laptop with the headphones already plugged in if you haven't done so before, and try directly after boot before doing anything else. I.e., make sure
Headphone Playback Switch and
Headphone Playback Volume are unmuted. Also make sure in
pavucontrol the stream is routed to the correct sink.
Additionally, please provide again the output of
pacmd list-sinks in the pastebin after unmuting.
Last thing to try is to enable
Auto-Mute Mode, unplug headphones, save a copy of
amixer -c0 contents in a temporary file, plug in headphones, again save
amixer -c0 contents in a different file, and compare with