I'd be willing to bet an open circuit evap sensor would stop the compressor engaging if it defaults to -40 like the others. I haven't confirmed that on a P38 though - but otherwise the HEVAC has no way of knowing how to cycle the compressor. Normally it cuts out at about 4c and back in at 7c, regardless of how you have the temperature set on the HEVAC itself. If you have both sides set to 'Lo' it will still only cycle in that window - otherwise it would risk a freeze up and flood liquid refrigerant back to the compressor and likely cause a big bang as the compressor chugs something it can't squash any more :)
Being an early one as you say though, it may genuinely just be a regas but eh, if it works reasonably well most of the time in his climate then I'd think charge should be okay. The other possibility is that on a properly hot day... if its overcharged, the high side pressure spikes and the high limit is cutting it off. That could be hindered by a dead condenser fan(s) or faulty pressure switch not bringing them on at all or at high speed. The high side limit is then hit, the pressure switch goes open circuit and the HEVAC will see it as a fault and disable the output, so no LED.
Because I have no viscous fan, here in the UK I have had my fans come on at high speed on a hot (35ish) day when first cooling the interior down - had to wonder what the hell the noise was to start with.
Does it work at all to start with on a hot day Paul?
If not... I'd personally be suspecting a wiring issue especially down by that footwell connector. The annoying thing is, that kind of issue will also raise it as a fault that disables the output... Perhaps a regas is the easiest place to start in this instance without diagnostics to ensure a proper charge - and then perhaps look at bypassing that connector for the clutch wiring to rule it out.
Sorry to throw more possibilities out there... always difficult to diagnose something over the internet.
That said if you want to fly me out to you, I'll happily bring diagnostics and recovery/evac/recharge kit with me to diagnose and regas it once we find the problem. No charge, just cover my travel costs :P
Southampton with a Nanocom for Thor/GEMS P38s
1996 4.6 HSE, then became a 4.0, now cubed.
1997-8 4.6 HSE Motronic/Wabco prototype vehicle. Now M57 powered. Still auto.