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Besides testing every cable for continuity (and ensuring nothing is shorted out) with a multi-meter, I try to test cables with their matching headphones and sources. I've got a lot of gear available with unique connectors on, for exactly this purpose!
When testing that stereo markings are correct, I use a test file to determine left and right channels are correct, before playing back some actual music.
In my personal collection, I have the following items:
2.5mm Locking: Audio Technica M50X & Sennheiser HD558
2.5mm Locking: Sennheiser Momentum
HiRose 4-pin: MrSpeakers Alpha Dog & MrSpeakers Aeon Flow
Mini XLR4: Audeze LCD-2
HD-600 Style: Sennheiser HD660S
TH-X00 Style: Fostex TH-900 mk2
3.5mm Dual Entry: Hifiman HE-35X
2.5mm Dual Entry: Modified AK K550
Beyerdynamic 7-pin: Beyerdynamic DT250
Mini XLR3: AKG K702
XLR4: Topping D90
XLR3 x 2: Topping D90 via adapter
Pentaconn (4.4mm): Topping D90
6.35mm (1/4"): Topping D90 & Icon Audio HP8
2.5mm: Sabaj DA3 & Questyle QP2R
3.5mm: LG V20 & Sabaj DA3
And likely a few others I've forgotten. I'll do my best to keep this updated if I get any new connectors for testing!
For science it's important to listen to music - At the time of writing this, I test using Now is the Time - embedded below- because I love it, but any music will work for this. It's a song that gets me moving - and that's great, because it helps me discover if there's any cut-outs when moving about using the cable.
As per usual, if I find any issues with the cables I will immediately stop to fix the cable, and start the testing process again from the beginning.
Shoutout to Packy Lundholm for making great music. Go check out his Bandcamp!
Note: I'm not affiliated with Packy, I'm just a fan of his work.