I think I've done this before with mapping a network drive in windows and scripting something like this:
tabcmd get "/workbooks/workbook1.twbx" -f "Z:\Tableau_Workbooks\workbook1.twbx" -u username -p password -s "http://serveraddress" -t sitename
Z: being the mapped drive location.
File/user permissions for your share drive might need to be configured properly so that there won't be an Authentication Prompt when trying to access the drive from another computer.
Save the script as a .bat and create a schedule in Windows Scheduler or another third party automation tool that will run the .bat file.
There might be better approaches floating around.