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I generally buy everything from a few places on ebay, like Kenable or VisioSound. But for metal adapters like that I don't think cheap necessarily means unreliable. I'd go for this: https://www.ebay.co.uk/itm/Metal-3-5mm-Stereo-Socket-to-6-35mm-1-4-inch-Mono-Jack-Plug-Adapter-003440/261401003895
which should do the mono to stereo you'll need for headphones, whereas the two you linked are stereo to stereo.
I asked
I'm trying with a stereo 1/4 to stereo 1/8 adapter, one of these: https://www.gak.co.uk/en/electrovision-f382a-stereo-mini-jack-to-stereo-jack-adaptor/904313 but no success with a couple of different sets of headphones.
In both cases if I pull the headphone plug out of the adapter part way I get sound through one side of the headphones, so assume the amp out is working
Just a crap/ dodgy adapter?
Try another adapter (https://www.amazon.co.uk/UGREEN-6-35mm-Adapter-Female-Headphone-gold-plated/dp/B01D82XXGO?ref_=fsclp_pl_dp_1 maybe) or even the 1/8 to 1/4 cable. Or both?
Actually, the question is, from where or what brand is recommended for simple headphone cables and adapters as the cheap stuff is unreliable?