Sounds like condensation- is there water on the equipment similar to a glass of ice tea in the summertime?
Do a test- wipe up the water, put a piece of paper or towel under the suspect. Time the drips.

Thank you for the reply. But it definitely is not just the condensation. The leak is relatively slow, but it comes from the outlet opening under the control circuit box. I put a small bowl below it, and I have to empty the bowl once every two days, or it will overflow. So it definitely is a real leak. Any other thoughts?

Other thoughts? Sure! *%^$((!!!
OK then, maybe you'll get lucky- if the box (pressure switch) has no exposed electrical wire sticking out,(and it shouldn't), see if you can rotate the box clockwise (looking down on it)to the extent that you don't strain any wire.
That pulls the threads up on the tapers and might stop your leak.
If that doesn't stop it, you'll have to close isolation valves, kill the power to the switch, undo the wire connections, unthread the box-making sure you back up (hold) the nipple so it doesn't loosen the next connection- and either re-tape or re-dope the connection. Reverse order assembly.
While you have the switch off the nipple, verify there isn't any gunk or other blockage in there before re-installing.
The rust inside the pressure gauge happens so often manufacturers must put it there. Actually, just a cheap gauge. As long as it articulates cut-in and cut-out pressures approximately, it's OK.

Thank you so much, alphonse. You provided very good and detailed instructions. I have to try it out, but it makes good sense. Will get back to you. Thanks so much again.

I agree regarding the pressure switch but if there's rust in the gauge, I think it's a good indication it needs to be replaced, although I've seen a rusty pool pressure gauge go on for years, but I wouldn't trust it. A good quality, oil-filled stainless gauge would be better. You might also want to test your water to see if it's aggressive and causing the corrosion, if your system is only 3-odd years old.