Fatigue and second jobs I havent seen it tested - but you probably can.
But you would need to put it in the employment agreement that any secondary employment needs to be approved and agreed by the employer prior to the employee taking up that second employment. Simplest that way.
The alternative is to renegotiate the employment agreement at a later date and have the clause inserted by mutual agreement.
Any secondary employment not approved could be ground for termination. I'd probably run with a breach of trust and confidence line. Though I'd give the employee an opportunity to remove themselves from that secondary employment first.
And ACC, should push come to shove, is a valid reason that helps an employer coming to a justifiable position. An employer shoudlnt be exposed to unknown business risk they can't manage. Claim costs are one aspect that ACC looks at when assessing an employers experience rating. Along with claim numbers. So 1 impaired worker having an accident can impact an employers experience rating / discount/ penalty. Of course - your wouldn't run that as your sole line of argument.
On a side note, any policies introduced without consolation and agreement with employees that impact on employment can leave an employer vulnerable if they choose to enforce those polices.