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Thank you so much for all the great advice! What a nice community! :)
I pushed out the pins from the 4-pin connector using a SIM tool:
I bought a 12V DC power supply with adjustable voltage (3~12) so that I can adjust the fan speed to my liking (noise, temps). The power supply came with a bipolar terminal. How in the world could I be this lucky. No need to carve any wires here (although it would have been nice to finally learn how to do that too...):
I put back the sense and control pins into the connector in order to avoid accidental shorts and what not. I have no idea why ground goes into the negative node, but it was the only plausible configuration, since the power simply has to come from the positive node, according to conventional current:
And voila! I have no idea why I'm unable to upload the GIF of my fan spinning, so you'll have to take my word for it.
Thanks again!
Electronics are complicated. Ground = negative node in most circuits. Unless you have studied electronics explicitly, most prior explanations you have heard are just good enough approximatons for whatever thing it was about.
Thanks! Yeah, I'll leave it at that now and just enjoy that it works. I've recently been studying the very basics just out of curiosity, but when they started to talk about earth being a giant sink for electrons, they lost me (for now). I'll definitely pick it up again next month. ๐