Take a close look at the smaller studs with nuts and labels. The one on the left says IGN. This is a key signal to instantly energize the voltage regulator. Hence the "low turn on".
The terminal on the RIGHT is labelled REMOTE SENSE. Therefore this is NOT a so-called "one wire" alternator.
The voltage AT THIS TERMINAL MUST BE EXACTLY THAT AT THE BATTERY BANK. If this terminal voltage is LOWER than at the battery bank the alternator voltage will rise.Therefore my guesstimate that you have a 2500 - 2800 series JB is incorrect. The 79000 voltage regulator part number is similarly incorrect.
You absolutely must determine if there is a VOLTAGE DROP between the alternator output stud and battery bank. And similarly between the alternator bolt left side NEGATIVE stud and the vehicle engine then the vehicle chassis.
Most of these checks can be done right at the rear of the alternator.
There is a frighteningly high percentage of possibility that NOTHING is wrong with the alternator and voltage regulator, and the real problem lies in the voltage sensing wire and connections. If the voltage at the alternator positive terminal and the voltage sense lead terminal read the same or very close, the regulator would then be BAD. If the positive terminal reads >.3 volts than the sense terminal then the sense lead wire is bad. Theoretically this sense wire should be connected to the CHASSIS battery positive terminal. They may have connected it to any terminal in the main starter cable routing. Don't screw with it - there are lots of places to connect this wire. In a pinch run a wire between the sense terminal and main alternator + positive (5/16") bolt output terminal.
Leece Neville (Actually Prestolite Co.) tried to get cute and access remote voltage sensing for line loss compensation to the batteries.
In a HEARTBEAT I would TRASH this regulator and convert to a Transpo 79000S or 79000HD regulator. The Leece Neville 79000 regulators do not turn on at low engine speeds, the Transpo regulators do just that. LN voltage regulation design has always been their weak point.
To try and compensate for disaster level volt-drop in the main charging cables is STOOOOPID*. Fix the cables. Prestolite screwed up the LN alternator the moment they bought out the company. Prestolite couldn't screw up the Motorola 10-255 J-180 foot alternator any more than Motorola had from the get-go misdesigned it before similarly selling out to Prestolite.
Marion Hovermale listened to me about remote sensing in the Delco CS series alternators and the regulators were redesigned to automatically switch to INTERNAL ALTERNATOR VOLTAGE SENSING if external sensing is compromised.
Grab that hand-held multimeter! I will walk you through the troubleshooting and the fix, step-by-step.