To test battery voltage the battery needs to stand overnight then measure voltage without waking the car up.
13.65 is probably to low with car running, these cars and many other modern ones run at mid 14s to just over 15 volts, these days mine pretty much exclusively gets used for the short daily commute of 5 miles, and the alt runs at 15/15.1v all the time, only time it drops to under 14v is on a longish run.
In the winter I stick the battery on a trickle charge overnight almost weekly to try and keep it in good condition.
The diesel alt is a clever sod and is told via a pwm signal what rate to charge at by the engine ecu, guess v8 one the same? I believe it has its own fuse, also worth checking engine and battery earth leads.
Battery and alt failure is a common thing on the d3/4 forum.
Very few d3/4 owners on here, certainly no d3 no owners apart from yourself.
