So I started looking for the pressure switch, and no, it wasn't under the cover with a wingnut like I saw in a youtube video, but it was under a black cover on the heater, which had I looked at it for 20 seconds, would have been an obvious place to check, since it was slowly dripping from the base of the cover. After taking the cover off, this is what I found:
I took another pic of the label to get the model number:
I'm still searching for a replacement, but will update here with what I find to swap it out with.
Update 10/22/2021 - I contacted the manufacturer and they provided me the info on the TecMark Model 3037P-CX pressure switch. They advised that it was an older model for a company (which made the spa) that is no longer in business, but said that I could replace it with either a "4037P, or a 4010P", but also warned that I would have to "calibrate the switch on site." They also noted that the "CX" specified that the original switch was set to change contacts (switch) on a pressure fall (edit) at 2.5 psi (+/- 0.5 psi). So I will set the knob on the pressure switch to 2.5 psi to test it.
That was good news since I have purchased a 4010P, which looked like it fit the spec and was plastic (so it won't rust out), and has a range of 1-5 psi. This is the one I bought. It can be found a few bucks cheaper at other stores, but I have prime so shipping makes up for the slightly higher price. My local spa place said they had some that would be compatible for under $40, but I wanted to make sure I got one that was at least OEM quality.
It should be noted that the way this switch works, simply replacing it without adjusting the pressure is not safe and likely would not work. My understanding is that this switch is designed to trigger when water starts flowing through the heater element, and that is a safety feature. It lets the processor know if there is a fault with the pump, and to shut down the heater (if no water is flowing over the heater). That way the heater will not keep running with no water flow through it.
After watching several youtube videos on this subject, I learned that there are some spas which use temperature probes to measure a differential of temperatures between the input and output of a heater element to perform a similar check. But my Dad's spa shown here only has one temperature probe clamped to the heater, and one pressure switch which is also installed in the heater housing. Based on what I have found regarding the error codes, I think the PS2 error he was getting right off the bat when turning on or resetting the spa, indicates that the normally open pressure switch (NO) was triggered (closed) with the pump off. That is odd though, since it appears that there is no way for it to have been closed having the mount for the switch broken as it was. Still it's clearly worn and faulty, so I will replace it and go from there if new codes pop up afterwards.
Update 10/28/2021 - My Dad installed the pressure switch and said it cleared the error. I had set the switch to 2.5psi prior which is what I think the old one was set for. From what I read, the spa will do a check every 96 hours and pop a PS2 error if it detects that the switch is on with the pump off, so it will be a few days to be sure it will not have a further problem, but he said he did a reset and did not see the error which is good news.