Drive to garage with a bad/low charge battery

A twelve volt battery is essentially six 2.1 volt batteries connected in series and sharing the same case and electrolyte. At full charge you will see 12.6 volts. You seeing 10.6 volts shows a single dead cell in that battery.
Being a modern vehicle with a high powered alternator it will likely make the trip but it will be a load on the alternator. If you have any way to bring a new battery to the truck, versus driving the truck to the battery I would opt for bringing the battery to it.

Or you mentioned that you jump started it, could you borrow a battery to put in it just to get to the shop and replace the bad one? As long as it is a twelve volt battery that can hook up it will work. That would take some of the load off the alternator.

Thanks Steve. You mentioned above for a maintenance free battery the cells "sharing the same case and electrolyte." Just for my own enlightenment (and maybe others), is this different than for a "serviceable" battery where, and correct me if I am wrong, each cell is totally independent of the others and can be checked separately for state-of-charge (specific gravity)? I had read that the monitor (green) dot of a maintenance-free battery was only for the cell it was mounted over. More correctly then, is it for the whole battery? And, in my situation then, was the green dot indicating that the electrolyte state-of-charge of the whole battery was good despite there being a bad cell? Alan.

It depends on the battery type. In automotive wet cell batteries the case is one piece, inside it has dividers for each cell. The plates set in each cell and are soaking in the electrolyte. The dividers are one item that makes a big difference.

On some batteries the dividers come all the way to the "top" of the battery and you have individual cell covers with vents in each cover. These are the batteries you can easily check and add electrolyte to. These days they are in heavy trucks and equipment and the lower priced motorcycle type batteries and are considered a serviceable battery. In theory you could drill a hole into a cell, drain it and the electrolyte in the other cells will not change.

Next you have the "low maintenance" batteries, basically the same as above but these have the cell covers made in one piece, if you open them you will see that each cells fill point has a slot that allows the electrolyte to flow to each cell and keep them all "full" these also share a common vent between the cells.

Then you have the maintenance free" batteries like yours. It has the same features as the "low maintenance" batteries but they use a sealed case with a system that traps the water and electrolyte that does "boil off" while the battery is charging or heats up. That trap returns the electrolyte back to the cells when the battery cools down. These also have spark arresters and traps in the gas vent systems that are supposed to lower the amount of hydrogen gas emitted while charging and "prevent" battery explosions if the gas were to ignite.

In both of those drilling a hole into one cell will drop the electrolyte level in all of the cells down to the top edges of the plates because that is usually where the ports are that let the cells fill evenly.

Some (mostly Delco) have an "eye" which is nothing but a tapered piece of clear plastic that sticks into the top of a cell and shows if the electrolyte level is okay. It does not really tell anything else. Because it is above the slots in the fillers it shows the level across the tops of the flooded cells. These will not work on the individual cell types because you would need one eye for each cell.

Then you have the AGM style sealed units. These use a material between the plates that absorbs the electrolyte and prevents it from spilling out, these are sealed and can in theory be mounted in any position without leakage.

In your case, I doubt the electrolyte is the problem, more likely is that one of the cells has shorted internally, either from poor construction or mechanical damage.