Just to draw a close to this, it looks like the EAS compressor was at fault.
The flat battery was a red herring. The fuse was always blown, but because my wife thought she'd left the lights on I assumed the battery was at fault when it wasn't. There's a lesson to learn in there somewhere!
I've disconnected the EAS compressor and the fuse has stopped blowing. I'll swap it out with a spare and refurbish this one if I can.
Do we have a "preferred supplier" of compressor refurb kits. I'll always go for quality over price.
If the compressor is blowing master fuse 2 it is either seized solid or a dead short and may need more than a refurb kit. Take it out strip it and see what you find. Maybe a new one will be needed.