Colin,
Yes, it's very near the battery. The pump generates a HUGE pressure - something like 260 bar - and there is a pressure vessel (like a small globe) which retains the pressure. The pump has a pressure limit switch attached to it (it's green) which has been known to fail. If this happens the pump fails to switch off and is in grave danger of self destructing if it runs for much more than 2 minutes. It can get VERY hot and will melt some of the pipework and will eventually leak brake fluid into the luggage compartment. The pump is VERY expensive to replace although the switch and pressure vessel less so.
Before you start looking for other possible problems it's crucial that you confirm that the pump operates correctly and switches off (and back on).
IIRC failure of the hydraulic pump usually results in a very hard brake pedal - not soft as you describe. So it may be that the problem is elsewhere.
Regards
Dave
BTW Colin, it might be useful if you could confirm WHICH light(s) come on. Do you get the gong at any time??