When a CH100 approaches the maximum current output, does the voltage stay at a constant 12 V up until that point? Or does the voltage begin to taper off as it reaches the maximum current output?

Actually, the current flows up to the maximum amount of amperage based on whether the battery will take the charge or not. The internal resistance of a lead-acid battery increases as it reaches a full charge. The charger/regulator must perform two operations when charging a battery:

• Give the battery all the current it will take when it is in a discharged state.
• Limit the voltage across the battery to a set value based on temperature when the battery reaches a full charge so as not to overcharge the battery.

The voltage rises as the voltage in the battery rises. When the battery voltage rises up close to the voltage limit of the charger, the voltage of the regulator is limited. This causes the battery to take less and less charge (less amperage) because the voltage of the battery and the regulator get to be so close that no more current can be forced into the battery.