LOW VOLT IN THE 12 VOLT RANGE

No. Cell in a home charges on 110 volt. Car voltage is 12 volt. When you charge in a car your charger converts the voltage.

If test light is a 12 volt light tester AND ILLUMINATES BRIGHT it shows that a component is actively trying to complete a circuit and yes drawing power causing a drain on your battery, now if test light illuminates low, possibility could just be ecm memory or antitheft system active . either way this test should only be done with a 12 volt test light as if you use a 5 volt (computer friendly) tester , false light will have you chasing a ghost. trust me. that trick helps by checking for parasitic draws a 12 volt tester does not illuminate when keep alive memory voltages are present . those voltages are not enough to drain over night. good luck

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with the engine running use a volt meter to check battery voltage with the head lights on, should be around 14 volts on a 12 volt system, if 12 volts or less the regulator or alternator is at fault . if around 14 volts there is a drain or short, the battery could also be faulty.

11 1/2 to 12 1/2 is not charging . That's less then battery state of charge , Battery stat of charge should be 12.6 volts , when charging with a volt meter you should see 13.1 to 14.1 volt at the battery posts . Is there a battery symbol lit on your instrument cluster ? Is there battery B+ voltage at the wires hooked to the alternator How to Test an Alternator

I would say that the battery is flat or old and wont hold a charge, or the terminals are dirty. probe the terminals with a volt meter around 12 volts ok ,if little or no voltage probe battery posts 12 volts ok , if voltage ok now terminals dirty, if no voltage battery flat or dead.

An unloaded reading of 10 Volts on a 12 Volt car battery is considered dead. There are 6 cells in a typical lead acid (car) battery - each provides 2 volts. They are internally connected in series to provide 12 volts on the + and - posts. If one is cell shorted out - you'd see 10 volts if fully charged. Trickle charge the battery for 24 hours and measure voltage again. If 12 volts, bring it to be load tested. that will tell you the true state of the battery.

the low charge # @ gauge could be caused by bad ground or high resistence in the wireing harness. Don't think it has anything to do with your 4x shifting prob I would check 4x switch and electric motor on transfere case.

ok when the pcm detects something wrong whit the charging system the pcm show you in your board CHECK GAGES if this is not on, dont worry about

If your getting power at the headlight wire harness, then it's going to be the bulb it self, but make sure your checking the right 12 volt terminal at the plug. There should be three terminals there, there is a ground, 12 volt low beam, and a 12 volt high beam. If both the low and high 12 volts are getting power, then it's going to be the head light bulb it self that has reached the end of it's life time since the day time running lights are always on which is the high beams. Good luck and check the fuse box under the hood by the battery. 

A 12 volt battery is actually 13.2 volts fully charged. If you are reading 16 volts, you are probably getting extranious voltage from the system somewhere, especially if the vehicle is running when you check the voltage. The alternator will put out about 15-18 volts to charge the battery normally, and yours may put out 28-32 volts to charge them in series, but the batteries, when disconnected, should never read more than about 13.2 volts each. Typically, it will read about 12 1/2 volts when disconnected. COMPLETELY DISCONNECT BOTH OF THE BATTERIES. If you still read 16 volts when it is disconnected, you must have a bad meter because the battery can't produce that much voltage, no matter what. (Six 2.2 volt cells connected in series inside the case.) Put the meter on a known good battery on another car that is not running and see if you get the same reading. It sounds like the other battery is almost dead, regardless, and it sounds like your series/parallel switch may be malfunctioning. (That is the switch that puts the battery in series to run the 24 volt starter, then puts the batteries in parallel to run the remainder of the vehicle on 12 volts. This is all assuming that you have a diesel vehicle with a 24 volt starter and that is why you have two batteries.