Sure, this process can be automated. We just need to see the auto-processing filter for this purpose:
Finance > Invoices > Charge > Auto-Charge Filters > Add.
The following options allow you to create a custom filter to charge the right customers.
It if possible to filter by Partner, Location, Payment type (CC, PayPay, Cash etc.), Invoice status. Customer ID option allows charging only specific customers. Please, set the desired payment system in External handler field.
Those customers that have ‘Cash’ as a payment type will not be charged in case you set ‘CC’ in the auto-charge filter.
Should you have any questions feel free to ask!