Two items to report in this post.
PA Equaliser appears to be operational
pactl load-module module-equalizer-sinkloads the equaliser module as expected, and presents an extra entry on the relevant tabs of PA Vol Ctrl called
FTT based equalizer on Built-in Audio Analogue Stereo
I have yet to play with this new option, but it appears to be a means of equalising the output volume level for the various different devices.
Much more to do to find out what exactly one can do with this.
Very happy to see it functioning

****
This second part is a little more involved.
My built-in sound card is an nVidia MCP51 High Def Audio, which uses the snd_hda_intel driver.
The card has two MIC inputs and a Line input .... but those are switched off for the moment.
It also has on the front of the PC, in addition to the front MIC input, a Headphone socket.
It is the headphone socket and speakers which I want to warble on about.
I have never actually used either of those front panel connections until today, because I was using a USB wireless headset with MIC so had no need of them.
So today I got hold of a $5 wired headset with boom MIC to test. The MIC tests went OK, but not the headphone tests. In the following part I attempt to describe what I met with. I will try to make it clear ..... but I am not really sure myself about some things ..... anyway here goes .....
**
I am using pavucontrol to view what is happening and to try to control the streams and devices.
Starting with the Headphones chosen as output port (Output tab of PA Vol Ctrl)
I issue the command
pacmd list-sinksThe relevant output is at the very bottom of the info
<snip>
ports:
analog-output: Analogue Output (priority 9900, available: unknown)
properties:
analog-output-headphones: Headphones (priority 9000, available: unknown)
properties:
active port: <analog-output-headphones>
*Note the active port is 'headphones'
Now I change the Output Devices port to Analogue Output port and run the same command again
ports:
analog-output: Analogue Output (priority 9900, available: unknown)
properties:
analog-output-headphones: Headphones (priority 9000, available: unknown)
properties:
active port: <analog-output>
As can be seen the output port changes to the speakers.
So I believe PA is doing its job ..... changing the active port for the sound stream, from headphones to speakers and back again, as required.
Unfortunately although PA appears to do its job in directing the sound stream to either
speakers or headphones, the result is anything but satisfactory.
The sound stream goes to both!!! 
Further .... although there are two - apparently - separate settings for the volume on headphones and speakers on the output tab, it seems that because the sound stream is going to both, the volume set on either is also applied to the other ....... this seems to be a side effect of the main problem.
if I choose the headphones and set a volume level, that volume level is also applied to the sound stream going to the speakers ......
if I choose the headphones and set a volume level, that volume level is applied to the sound stream going to the headphones.
It appears I can set different volumes for both, but whichever port is chosen, the preset volume level for that port is applied to the sound stream going to both.
All of that seems to me to be a result of the failure of the system to direct the sound stream to only one port and not both.
Even if speakers or headphone could be individually muted that would suffice for most situation.
I cannot do that from pavucontrol either.
The sound stream is going to both ports regardless what PA is telling Alsa

The installed Alsa system is Ver 1.0.25 ...... but because I never tried before I have no idea if this worked on previous versions.
So, I tried Alsa to see if it 'sees' the headphones as a separate port and here is what I got when looking for a list of 'PCM' devices ...
[user@XPS ~]$ aplay -L
null
Discard all samples (playback) or generate zero samples (capture)
pulse
PulseAudio Sound Server
default
Default ALSA Output (currently PulseAudio Sound Server)
sysdefault:CARD=NVidia
HDA NVidia, ALC1200 Analog
Default Audio Device
front:CARD=NVidia,DEV=0
HDA NVidia, ALC1200 Analog
Front speakers
surround40:CARD=NVidia,DEV=0
HDA NVidia, ALC1200 Analog
4.0 Surround output to Front and Rear speakers
surround41:CARD=NVidia,DEV=0
HDA NVidia, ALC1200 Analog
4.1 Surround output to Front, Rear and Subwoofer speakers
surround50:CARD=NVidia,DEV=0
HDA NVidia, ALC1200 Analog
5.0 Surround output to Front, Center and Rear speakers
surround51:CARD=NVidia,DEV=0
HDA NVidia, ALC1200 Analog
5.1 Surround output to Front, Center, Rear and Subwoofer speakers
surround71:CARD=NVidia,DEV=0
HDA NVidia, ALC1200 Analog
7.1 Surround output to Front, Center, Side, Rear and Woofer speakers
I see nothing about a headphone port ....... in fact any port numbers ..... another track to follow it seems ......

So I had a look at the list of 'devices' ....
[user@XPS ~]$ aplay -l
**** List of PLAYBACK Hardware Devices ****
card 0: NVidia [HDA NVidia], device 0: ALC1200 Analog [ALC1200 Analog]
Subdevices: 1/1
Subdevice #0: subdevice #0
card 0: NVidia [HDA NVidia], device 3: ALC1200 Digital [ALC1200 Digital]
Subdevices: 1/1
Subdevice #0: subdevice #0
So, it appears to me, at this time, that the Alsa driver is at fault.
PA recognises the presence of a Headphone socket; sees that it has a separate port to the speakers; and apparently sends the sound stream to the correct port ........ but Alsa does not deal with it properly.
In fact PA seems to indicate that there is something amiss
<snip>
ports:
analog-output: Analogue Output (priority 9900, available: unknown)
properties:
analog-output-headphones: Headphones (priority 9000, available: unknown)
properties:
.... that is of course conjecture on my part based only on what I have reported above ...... a lot more investigation is required to be sure of anything .....
More investigation is needed to try to determine what is causing the problem and then hopefully what might be a 'fix'.