An air carrier flight crew reported turning down the wrong taxiway in STL because of fatigue and distraction.

Narrative

I was informed that myself and the First Officer would be ferrying an aircraft for repairs. When I talked to crew scheduling I had asked them to ACARS us our hotel and deadhead flight information. (I assumed I would receive the information while we were airborne). After all the maintenance paperwork had been completed and dispatch release had been received we pushed back from the gate. We received our taxi clearance: 'left turn on Charlie; left turn on Sierra taxi to Runway 29.' Both pilots had their charts out and discussed the taxi route. As we taxied we completed the before take off check list. We were approaching Taxiway S when we received an unexpected ACARS message from crew scheduling. Both pilots looked down at the message while we were still moving. I taxied past S Taxiway and turned left on Taxiway Tango to Runway 29. At no time did we cause a traffic conflict with other aircraft or ground vehicles. The event took place due to the onset of fatigue; a non-standard operation and a minor ACARS distraction. In short it was a long duty day; I was tired and felt a self imposed sense of urgency to get the plane to the maintenance station for repairs.