Those ‘funny wee connectors next to the test socket’ are a royal PITA. Fiddly to use, not ‘craft sensitive’
The wires do NOT need stripping, the act of closing the ‘catch’ if the wires are set up right, will make the metal part act act as an IDC as the wires get pushed home.
Without wishing to sound rude … you are setting it up correctly aren’t you ?
Use a single twisted pair .. blue/white and white/blue for instance … untwist the pair apart for a few centimetres, and pull the wires to makes as straight as possible. (Don’t bother with a bell wire unless the phone the other end is archaic)
Lift the clear ‘cam’ part (it comes out to about 40 degrees) hold both wires some way back from the end and guide the wires into their correct holes in the cam .. blue to 2 white to 5 is the usual way. They should pass through the holes, through the 3mm gap after, and into the locating holes after that ….. whilst still holding the wires in position, use your other hand to to close the cam and wires therein onto the IDC. It should click shut quite happily, if it doesn’t … you’ve done something wrong.
If you have done it wrong, remove ALL wires, trim a couple of mm off and try again.
If you are anywhere near as decrepit as me, plenty of bright light, your glasses, and a swear box are essential.
Give me a Krone termination every time. These ones are cheap and [censored].
Since you often have to do the above faff whilst head down, [censored] up, preying to the great God telephony, I find it simpler to correct a few inches of wire into position before attaching the NTE to the back box … you can then gel crimp these wires onto those of the extension wiring going away, thus avoiding a lot of the heartache these poxy things cause ….. but this depends on you having crimps, crimpers etc readily to hand.