score:3
The exact limitations of the eVisitor (subclass 651) visa are listed in the "Migration Regulation 1994" act:
651.611
Conditions 8115, 8201, 8527 and 8528 must be imposed.
The description of these conditions is spelled out in the Visa conditions section:
8115
The holder must not work in Australia other than by engaging in a business visitor activity.
8201
(1) While in Australia, the holder must not engage, for more than 3 months, in any studies or training.
8527
The holder must be free from tuberculosis at the time of travel to, and entry into, Australia.
8528
The holder must not have one or more criminal convictions, for which the sentence or sentences (whether served or not) are for a total period of 12 months duration or more, at the time of travel to, and entry into, Australia.
Therefore you are free to study in Australia under the eVisitor visa, as long as you don't do it for more than 3 months.