G'day Scotsman & Jack,
If you have 13.5 to 14 volts at the battery I'm thinking it should charge - unless the old battery won't accept a charge. Might be time for a new battery.
The light remaining on is an odd one. I think there's every chance your on the right track checking someone hasn't mucked around with the wiring. I'll pull up the wiring diagram and have a look a bit later in the day.
Cheers,