Jaguar Repair/extra air flow valve
Howard here is an extract from the European manual
I have worked on many different British, German and Italian cars and the relay pin numbers are universal in their meaning. #30 pin is a power in. and #87 and 87a are power out. Some relays have power out on both when the relay is activated and others may have power out to #87 and switch to #87a when active. There is usually a diagram on the relay case that will tell you what it does. You need to look at them and write it down. Then send me the diagram of each relay.
I suspect the diagram you have is not correct at all even though it is incomplete because it has some contradicting connections, especially on relay #1. It is powered and seems to also power itself. Unlikely for any relay to be wired that way.
If you could send me the little diagrams of the relays that have the 87a trminals I may be able to further unscramble some of it.
Your thoughts of a control for AC may be ok on a Euro car but the US version never turns the AC off even in the winter when heat is turned on. They keep the AC on to dehumitify the heated air and control temp by door blending and fan speed only. Another possible is Park to drive or neutral to drive.
Let me know.