First, understand what you have. The presence of pan and tilt should be easy enough to confirm, since there will be two sets of rotational movement mechanisms at 90ยบ. Zoom will likely be something bulky around the lens or a lens assembly that looks more complicated than you might expect for a fixed lens. Zoom is not always provided on cameras with pan and tilt.
As stated above, the first thing you need to do is see about getting the camera working. Forget about the pan, tilt and zoom for the moment. I wouldn't even worry about focus at the beginning.
To start off, look for any and every bit of writing you can find - stickers, PCB markings - anything that might provide clues about identification, connection pinout, supply voltage and polarity, etc. Take photos - but they will need to be better than the one above. (The lighting could be better - and whiter - but they REALLY need to be much sharper.)
Don't apply power to anything until you have a high confidence that you are connecting the right voltage and polarity .... and don't disassemble anything unless you have a specific reason AND have lots of photos to show you how it goes back together. (Take photos as you disassemble, to show intermediate steps.)
IMO, the tattoo supply is a better choice than a converted computer PSU - but it might benefit from adding a filter capacitor across the output (a few hundred uF at least).
This will be a challenging project, especially if you are starting out. It is also going to be risky - because one slip and you could kill it - and without some sort of guide (like a schematic) repair may be extremely difficult. This assumes, of course, that the unit is working in the first place.