Hi Dave,
I wish I could help with knowing what that fast idle button does. I had the
same questions with my HPE (au spec) when I got it. The a/c wasn't working anyway,
and seeing I didn't need it here, I removed everything. My car also has a clutch pedal
switch and also had a 2nd switch in the gearbox, subsequently deleted due to a g/box change.
I suspect the idle button/relay is something to do with servicing the engine without the a/c running, but
that's pure speculation.
Nigel