Powering a 4-Pin stock CPU heatsink fan with an external power supply

I have scoured this website and the rest of the internet looking for a solution to my particular issue, but as of yet I have not found an answer. If this is a duplicate question I am sincerely sorry, and I would appreciate being pointed in the correct direction.

I have an only Intel CPU heatsink with the stock Nidec fan that was discarded during a previous computer building project. I now have a new project where I require additional airflow so I decided to try and "re-purpose" the unused CPU heat sink fan for a cheap fix to my solution.

Everything I have read on the internet says to buy a 12V power supply, connect positive to positive and ground to ground and you should be good to go, but this has so far not worked for me.

I currently am using this Nidec CPU Fan and have wired it up to this Power Supply. Following this 4-Wire Fan Description (link 1 in comments) I have connected the yellow fan power wire to the red wire on the power supply and the black fan ground to the black power supply wire. The green tach and blue PWM wires have been left unconnected to anything and are simply hanging free.

When I connect the power supply to an outlet the fan "stutters" forward a single pulse like it is overcoming a single pole on the motor. I would estimate the turn is something like 30 degrees of a full revolution, but I have not measured this accurately. After the initial "stutter" or "pulse" in the right direction the fan stops moving. After waiting a few seconds the fan again "stutters" forward another 30 or so degrees before stopping again.

This behavior and the "simplicity" with which everyone else seems to be making these fans work leads me to believe that either my power supply is insufficient, or I need to feed a signal to the PWM wire. I found this YouTube video (link 2 in comments) where a guy just throws a big cap across what appears to be the positive and ground terminals of his power source and the fan runs. However, I am very unfamiliar with circuitry and his set up so I am not sure exactly what his solution is and if it will work for me problem.

This YouTube video (link 3 in comments) shows a pretty decent break down of how PWM and 4 pin fans work but I don't have a lot of fancy gear to hook up and generate the power signals he is using in the video.

My goal in the end is to keep my solution cheap! I really want to avoid building 555 timer circuit to control fan speed or anything crazy. I have access to a few capacitors from my father so I may be able to build a very basic circuit if a cap is all I need. However, if running this fan requires something more expensive/complex I will likely go buy a cheap 2 or 3 pin fan to replace the one I am trying to use, but again, looking for a near zero cost solution here.

Thank you for reading! Any help is very much appreciated!