Battery light on ......

[Jakemate]

You need to check current output to get a true indication of charging.
The voltage will drop a little when you turn on lights etc but the current will increase if charging correctly.
See if you can borrow an amp clamp and put it around the main battery pos or neg cable to check current.
If the current is ok I would suspect a duff warning light diode, if this is so your alternator will be charging correctly but your warning light will illuminate.
You could see if you can find a local alternator reconditioning firm to do a full alternator test.
If you strip the alternator you can check the diodes with a multimeter but you will prob rally have to unsolder it first.