Option 1 - assuming you're using one of the relay modules, wire the supply and control lines on the relay module to 5V, then wire the ground pin to PS_ON. This is how I do it on my Duet WiFi.
Thanks! That sounds like a plan! And PS_ON can handle being a ground?
On the neopixel header, I don't have D3 Mini, but believe you can take the neopixel supply from the Duet board if you are using an external 5v supply to power the board (the internal 5v regulator isn't powerful enough)
It's confusing because the Neopixel header has a "5v in" pin and not a "5v supply pin" like I would imagine. So I just assumed you run 5v to the LEDs from the PSU. But then what the heck is the second 5V_EXT_IN pin for? I don't think you power them from the board because I don't even see a 5v out pin that isn't attached to something else. There isn't really any documentation as far as I could find. If I had to guess I would say the second 5V_EXT_IN pin that's on the Neopixel header just goes unused but I have no way of confirming that right now. The only way it really makes sense in my head I guess is if that pin was really supposed to be 5v out and not in.
Update
I found the documentation! It wasn't linked from the other documentation so I had to search for it. Here is what it says:
Connect the LED strips to the 3-pin connector labelled NP_LED.
Connect the GND pin of the LED strip to the GND pin on the Duet NP_LED connector.
Connect the +5V pin of the LED strip either to the EXT_5V_IN pin of the NP_LED connector, or to an external +5V power supply.
Connect the data input line of the LED strip to the NEOPIXEL_DO pin of the Duet.
You will need to supply external 5V power to the adjacent 5V_IN connector, unless you connected the 5V line of your LED strip directly to an external 5V supply. The 5V regulator on the Duet 3 Mini is rated at 1A total and cannot be used to power LED strips.The maximum supported number of Neopixel LEDs in a strip is 60.
So that pin can also put out 5v from the other 5v input. I guess the pin name is just confusing.