I obviously misunderstood Dominic when you said ignition on position 2 - normally to me that means engine not running. If the engine was running and nothing happened when it should have done then it's fair to say your headlamp washers don't work at all. Could be a fuse, relay or something more complicated.
I do like to have AC working on cars that are meant to have it, my Volvo (predecessor to the Honda) had AC but the previous owner had the evaporator removed thanks to incorrect diagnosis on why there was no air coming out of any of the outlets from the heater! Turned out that fault was 3 dry solder joints on a vacuum control module which i fixed. I also sourced a replacement evaporator but never got round to recommissioning the AC on the Volvo.
I do however fully intend to source a replacement pipe for the AC on the Jag and get it up and running as it should be, only trouble is that for mine, the pipe in question is either NLA or the sharp end of £500, the jury is out on which pipe exactly it is! However, i suspect i could get a replacement made by Pirtek or a similar firm for considerably less.
Any news on the diagnosis of the EML so far?