That will not prove or change the problem. The issue is the VR "is it' getting full batt V so it can properly sense, is the VR regulating at the proper set point of nominal 14V (IE is it good or defective) or is there some wild card.
Steve why don't you try this. You have that VR pigtail. You will have to manually disconnect his test after shutdown, or it will draw current. Cut the blue wire at the VR pigtail, runa GOOD connection wire direct from the blue VR wire right to the big stud on the start relay. See if the battery settles down to about 14V. In other words, temp power the VR direct from the battery. Leave all other wiring connected as normal.