This issue has been going on for some time now, and I am at a loss as to whats going on!
Both my '99 and '02 do the same thing.
When the compressors are running, they "short cycle". By this, I mean they turn on and off in bursts of 15 seconds to a couple of minutes.
Looking at the compressor state on Nano, it shows compressor as "ON", and thermal switch as "NORMAL". It will do this from
stone cold, so not a thermal issue.....
I have several good compressors here, and they all do the same thing, so not the compressors.
The compressor relay is new, and it does cycle on and off with the compressor, so it is getting a signal to switch on and off.
If I wait a few minutes, the system will get up to pressure and the pressure switch will change state shutting off the compressor as it should.
I am looking at the EAS ECU, and I suppose the MosFet driving the relay is possibly thinking it is overcurrent and folding back the output? Looks like pin 8 from the ECU has that signal....
This is no major deal except that when the missus is doing short trips to the shops, it will eventually come up with an "Unknown Fault"
and go to extended height whilst flashing all 4 lights on the EAS switch. Probably finally runs out of air??
While I am at it, has anyone come up with an answer from Colin and his merry men about why the Nano displays an EAS fault as "Unknown"??? It can clear it fine, but not knowing why it faulted does not assist in troubleshooting!. Annoying, at best!

As long as the thermal switch stays normal, as you say, it isn't a thermal issue so the only thing left is the pressure switch. IIRC pressure switch state and compressor state are on different pages on the Nano screen, so you can't easily see if the switch changes state at the same time as the compressor kicks in. It might be worth hanging an LED across the compressor so you can easily see if they coincide. That would suggest a lack of hysteresis in the pressure switch but as you have two that are both doing the same thing, that doesn't make a lot of sense unless that is how they go with age? It should be closed at 140 psi and not open until it drops to 120 psi.

I can hear the compressor when it's running, and see Nano from where I have my finger on the relay to feel it click in.
The pressure switch is not changing state according to Nano.
Relay ~randomly~ cycles the pump but pressure switch stays open until the system gets to pressure, then switch closes, and compressor is commanded off.

?Try swapping relays?

So the question really isn't why does it suddenly cycle on for a short period but why does it stop in the first place if the pressure and thermal switches don't change state? My understanding is it should run until the pressure switch changes state so it stops and then only start again when the pressure has dropped. It is inhibited at certain times though which may prevent it from reaching full. Before I changed my compressor mounts so I can no longer hear it, I noticed it would sometimes run when sitting at a junction with the brakes on but stop as soon as I started moving.

I have tried 3 different known to be good relays. Same result.
Will dig into it further today.
I am going to look at pin 8 on the EAS controller to see if the signal comes and goes