Is it perhaps too simple to ask BT to fit a NTE5 socket because you do not have one. The joy of having one of those is that it is the master, you have the option of trying your modem in the hidden test socket, the socket that eliminates any internal wiring, so if things work there you know it is internal, or if it doesn't you can legitimately report it to the ISP.

Not sure how receptive BT are to fitting a box but when you report a noise fault they insist you try using the test socket, so perhaps if you claim you have noise (intermittent cos we all have them ) and tell them you have no NTE5 so cannot tell if it is internal or external they may fit one for you, hopefully no charge.

With a NTE5 fitted you have a certain method of establishing where the fault is, upside or downside of the box, and you can the get your internal stuff sorted out.

As suggested a local sparks or whatever can be far cheaper than BT.