Not to be that guy but the voltage shouldn't jump up, it should maintain under load or stay very close to the same. The amperage output should increase however. Technically if your only putting out 13.2v under no load your not likely to see it shoot up to 13.7 when under load. However a small drop in voltage is acceptable. That being said the 13.2v I referenced would be of concern in my vehicle.
taking lwg's comments into consideration, I've been testing a new alternator. The original had over 163k on it. No drives yet, but the 250amp alternator was putting out 13.8 at an idle at first start. Thanks are looking better. I initially noticed when I connected to the trailer with my battery connector, I was struggling to get those batteries up. When I plugged in, there was no change to the output voltage at idle. This leads me to believe I also had a weak alternator, moderately masked by my solar charger... I'll post up an update if anyone is interested. The previously linked graph will show the differences as time goes on.
Most notably, I noticed, previous to changing the alternator when accessories where running on the 2nd battery, I would see a voltage drop of about 1v. At initial glance, there is less than a 0.3 v drop when similarly loaded. No voltage drop, when plugging into the trailer batteries.
The alternator, which I have high hopes on, puts out a higher amperage at a lower RPM, via a smaller pulley and different diodes I believe. They suggested a 1" shorter belt may be necessary, if you hear any belt squeal. I'm hoping it will be fine with the existing belt, and at first glance there appears to be plenty of engagement on the tension device.
Yup. Sounds like the LR4 has a smart alternator and it should drop to about 12.8V, give or take (a nominal float voltage), when it decides the battery is charged and the load is light. It's an emissions, mileage, whatever feature that vehicles are starting to use. Throttling back the alternator reduces the load on the engine slightly, thereby increasing efficiency. Or so goes the theory. It should jump to 14.7V or so to charge, be that through regen braking, the alternator being told by the ECU to throttle up after starting discharge, turning on headlights/seat warmers/your 1000W boom stereo. Why the OP's truck is acting up is hard to know since there's a lot more players with their fingers in the punch bowl now than the old way with a dumb alternator and voltage regulator. But I would have thought the ECU would just say be in either low power or high power, so the 12.3V level sounds like a bad alternator.Just want to add this note for posterity - any comments not specifically relating to the LR4 platform and it's advanced alternator management strategy are irrelevant. This is not a D1 or D2 with a basic voltage regulator.
Is this measuring voltage and current at the battery or the alternator? What is the open circuit voltage of the battery, particularly after you've charged it and let it rest?