Looking for some Guidance Finding a Power Supply for a CrocSee CRS-7A016 Micro Water Pump (specs in post).

What did you hook up? You mentioned using cords? But first off, what you pictured, you need to make sure it's wired correctly. There is no standard for barrel jacks. The center pin can be positive or negative and the jacket and be positive or negative. If you're using a generic 5.5x2.1mm female barrel jack most generic 12v power supplies overwhelmingly do center pin positive and jacket negative. Once you get polarity correct check the amperage rating of the supply and the motor. Motors usually require huge in rush current to start and can easily trigger a short circuit protection on the supply output

Since the pump doesn't seem to mention it does the pump packaging/paperwork mention how many amps it draws?

Edit I found it. Load current < 350mA

I would think damn near any 12v DC "wall wart" would do it, but the adapter you have may not be the right size for what you have laying around.

Could grab something like THIS that comes with its own adapter.

no worries, something like this would be fine

https://www.amazon.com/JOVNO-100-240V-Converter-Transformer-5-5x2-5mm/dp/B0875WMYCX

a 12v 1A power supply is sufficiently basic of a component that i wouldn't worry too much about like getting a higher-quality one or whatever they'll all probably work fine