Follow-up message works like a cron job, every certain minutes it executes and checks your accepted connections.

It sends the follow-up message to people who accept the invitation, the ones that did not accept the invite will not receive the follow-up.

Note: We are currently working on adding the option to avoid sending follow-up messages to people that have already been contacted manually. This way, we'll avoid sending duplicated messages.

Does this mean I cannot have a follow-up message go to someone after a visit, if they did not accepted my connection request yet?

Exactly, can send messages to 1st degree contacts using the feature "Send message 1st degree" and it can send messages to 2nd degree with a personalised message inside the invitation.

But the follow-up feature is only available when someone accepts yout invitation to connect.

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