Needs further voltmeter testing before any sense can be made of this. Definition of "isolator" needs to be established. Finned box or tin can with studs type?
If it were me and I had only 5 minutes to diagnose I would measure voltage at alternator output stud then see WHICH battery agrees with the potential. If you have voltage at the alternator with a finned box (rectifier type) isolator, you've found your problem. DrewE's diagnosis makes the most sense. I made the mistake of brushing the back of my hand against the output stud of a Chrysler Squareback alternator that had gone open circuit full fielded. Vertical learning curve about safety.
Do this first
JUMPER WIRE across the isolator. Start engine. Check voltage at BOTH batteries. What have you got?
