You are right Phil, there's a lot going on under there. The ABS stuff and EFi stuff looks horrendously complex and I suspect that is most of it.
This is the first time I have taken the tank off, and TBH I have been a bit intimidated at the thought of taking it off as the Haynes manual goes to something like 18 steps but in the end it was pretty straightforward: remove the various panels and trim around the tank, disconnect fuel pump(s) power and lines, disconnect drain and breather pipes, undo the mounting bolts, remove air box intake, and lift, pull back, and off. It was bloody heavy as it was 2/3rds full but there's plenty of good grab points and its unpainted plastic so slightly less care can be afforded. I spent ages trying to work out how to release the electrical connectors, and then one of the mounting bolts was seized but the impact driver soon got it out (and I even realised t was a 5mm allen rather than the usual torx head). About an hour to get off and 30mins back on. A lot lot quicker next time.
Battery is still charging and I am edging toward it being a battery problem. The starter is just a basic charger and its difficult to f**k them up (and it was brill immediately after I first "fixed" it), the earths and various connections were all reasonably clean and bright. The only thing I can't then explain is why it wouldn't take a jump start - the jump leads were thin, dirty and hadn't been used in years, plus it was difficult to get a good connection on the bike battery due to all the extra cables attached. So it could be I didn't get much help from the donor battery - I hope anyway. I think I will get a Motobatt, UKGSER is full of good reports about especially for curing slow cranking of a hot engine - which where all this started.
Down to my mum's in the car tomorrow now.