I can imagine Greenfield buying their G65s without the starter motor, since in 1970 I think that would have been the usual specification for ride-ons in Australia. What I can't imagine though, is why they would then have fitted a battery to a pull-start magneto-ignition mower - it sounds completely non-functional. It is the presence of the battery that made me think this mower started life with a G65 fitted with a starter and an alternator.
As far as the alternator, or "charging coil", is concerned, the workshop manual shows it but I don't see it on the few G65 parts lists that are still available on-line, so it, and the starter, may have been optional rather than standard. It might be best to have a look at the engine, checking for signs of residual wiring that match the engine wiring diagram I posted previously. If any of that wiring is present, chances are the charging coil is still there and can be connected. Alternatively if you have any reason to remove the flywheel, such as to check the breaker points for example, you will see whether there is just an ignition coil, or extra wiring for battery charging.