Resolution
You need to install the Type III battery extension into the System folder. Do not remove this extension even after you have installed System 7.5 and the System 7.5 Update 1.0. The extension is on a disk called Battery Tools, which ships with the Type III battery.
Background
When the System 7.5 Update 1.0 extension loads, it replaces the PG&E (battery management) code. This PG&E code then reloads to the external battery charger. Because of this, the external recharger does not recognize the Type III batteries and you get the red light. However, the batteries charge fine in the computer itself.
Conclusion
You need to use the Type III Battery extension to get the external charger to work with System Software 7.5.1 (System 7.5 plus the System 7.5 Update 1.0) and Type III batteries.
These articles can help you locate the software (Type III Battery extension) mentioned here: