Where I am there are "standard" pushes published for each stand.
The pushback crews are required to know and carry an up to date copy of these in each tug and to monitor the GMC frequency.
For standard pushes the only instruction required from GMC is "push/start approved .............".
For non standard pushes the GMC uses whatever phrases clearly describe what is required.
Non standard pushes cannot be issued when hand signals only are being used to communicate with the pushback crew.
Seems to work well with few problems.
For a standard push no pilot instruction/message as to direction etc is required.