Looks to me like those two metal side clips hold the plastic cover on. They are visible from the outside, so should just press in.
 
EDIT: Curiosity, and impatience for a GFS reply got to me. Popped the cover off. Every looks and fees tidy. May look for a meter tomorrow, but no idea where to start with that. Tracking down flux core solder was bad enough.
 
at least I can bypass the kwikplug now to rule out the coil

OK, so I don't know what I'm doing here. At 16, I received a certificate in Engineering after passing everything except the electrics class. They let me move to the next level, but I had t change to Cnstruction, received a diploma an then a degree. I am still no wiser abut eletrics than my 16 year old self.
 
One thing I am not happy with GFS, is the pickups are not marked. I had to write GPS39 (Neck) and GPS40 (Bridge with a marker as I unbxed to avid cnfusion. They should be 8.4k for the bridge, 8.2K for the neck. Neck pickups are now REVERSE WOUND
 
Setting my cheap Chinese  meter to 20KΩ they read 8.83 and 8.78. So for all I know they are the same pickup. But the GPS 39 is wired White/Black and the GPS40 Back/Red. S the black wire is switched (would tht be reverse winding?).
 
So I am getting a stable resistance reading with both, so I assume the coil is good.
 
But I did notice this! Testing continuity
There are 3 connections. Hot 1 / Ground 3 /Shield(case) 4.
 
KPH 40 (the good one)
1>3 1704
1>4 No response
3>4 No response
 
 
KPH 39 (the bad one)
1>3 1695
1>4 1695
3>4 continuity (the meter beeps at me)
 
 
 

Opens the case to check for stray wires or damaged wire jacket. All was tidy.
 
Unsoldered contact 3 and measured. All readings now matched the good PickUp. So the error must be in the KwikPlug. 
 
Re-examined all the solder points and compared with the good PickUp. Then spotted the edge of a solder point making the smallest contact with the female jack
 
SOLVED!

Hehe... for not passing electric class, you done good! I'd wager you know a little something :) Glad to see you got it resolved!

Just a little a guess. Luckily I my school decided they didn't want me this week, dues to a Vietnamese event. So I had time to work through this problem in one flow. My Vietnamese prnuciation has imprved too, and took me an hur t track down a suitable multimeter.  With most shops comprehending "Đồng hồ vạn năng"
 
Next job - Sax neck recorking
Then - Flute foot re-padding
Then - Change laptop keyboard and RAM
Then - New LCD tuch screen in Camera
Then - Re-pad Alto flute
Then - Finish set up f new work laptop
 
Damn I needed this break

Moral of the story:
Phuck the quick plug!!

You want me to do what!?!
 
Actually I dn't mind the system, I just had a dodgy one. At least I was able to quickly switch tem to rule out my soldering. If I wanted t try the bridge in the neck its easy (especily as this is a Epiophone Dot (335 clone) and that harness is a pain to pull out the sound holes each time. IF I wanted to quicky try a humbucker/p90 combinations, its now pretty straight forward. AT GFS prices, if I lived in the US, I'd be really tempted to mess around more.
 
This demo sold me on giving a GFS a try

Pulling the electrics out of a semi is the opposite of fun, getting them back in again is even worse.

Having said that, on Gibsons and the small number of Epis I’ve worked on, if they have a centre block there’s a kind of hole in the bridge pickup cavity facing downwards towards the pots and jack socket. That hole is there to provide a way to get the electrics in and out rather than trying to get them through an f hole. Just remember to securely attach long bits of thin string to the switch and pot shafts and jack socket before you remove them and make sure the loose end of the string doesn’t fall into the guitar.

Then you can use the string to pull the parts back into place. Still time consuming, fiddly and annoying to do though.

No helpful hole in the centre block, just a  small one for both pick up cables to run through.
 
I had all the pots and the selector attach to a pencil with dental floss, with the washer and nut on the floss too, so I could pull the floss and tighten them back on again.
 
The whole job would have been much nicer with an extra inch or half of cable in the harness for each pot. I was glad to get the kwikPlug fixed and not have to drag it all out again to run a new cable bypassing the kwikplug.
 
So glad I got that mutimeter. I doubt I would have progressed otherwise, so cheers
 

I didn't think that far ahead when I put my old PAF PRO in the bridge on my Epi Dot, but found a simple needle and thread worked for reassembly with a magnet. Lesson learned though... string during the disassembly would have been a lot wiser. That guitar indeed has no access other than the f-holes. :(

Guitar looks odd now at a distance because that pickup is black and looks like a hole in the guitar :)