Big thanks to MarkWalsh for helping me with this one. Thought I'd share the solution for anyone else with a similar project:
Use this for the Custom Format Script in the 'CustomerName' field:
if (this.getField('BillingSite').value == 'Off') {
// Allow entry into field
this.getField('CustomerName').readonly = false
} else {
// Don't allow entry into field
this.getField('CustomerName').readonly = true
// Set field value
event.value = this.getField('BillingName').valueAsString
}
And use this in the Custom Calculation Script for the CustomerName field:
event.value = event.value
