Thank you for reaching out to Constant Contact API Developer Support. My team is here to assist outside software developers with questions about building into Constant Contact's API.
In order to select a contact list for your campaign via API, you’ll need to use the PUT (Update) An Email Campaign Activity request. I’m including our documentation on this request below. I would recommend checking with Make.com support to see if this request is available with their integration.
PUT (Update) An Email Campaign Activity:
Please have a look and let us know if you have any other questions!