Without knowing what engine, one doesn't know what charging system and test procedure to use.
Without having a schematic for the machine itself, one wouldn't know what electrical loads are placed on the charging system, which helps determine which charging system the engine may have.

90% of eX-Mark z turn mowers have a Kohler Command engine.

So I will go with that for now.

On the right (when sitting on the mower) of the engine. Look for the Rectifier/Voltage regulator. It will have two same colored wires and one of another color plugged into it.

Like in the photo.

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The rectifier will have two screws that hold it to the engine shroud. Loosen one of the screws and attach a 14 or 16 GA wire to the screw. Ground the other end of the wire to the frame.

Do not know how it works. But doing it will fix 99% of the charging problems on a Kohler Command engine. I have been running three of mine mine like that for 6 to 8 years and have yet to find a dead battery or experience any other electrical problems.

The ground strap (that goes to the missing shroud bolt not shown) has been standard equipment for a while. It is a good reminder though. Another good reminder is to either disconnect the regulator or the battery cable and then resume testing. This will allow the regulator to reset itself. If there is no output from the stator, pull the flywheel before ordering parts as Kohler seems to have the wayward magnet problem the other 99% of the time....