Enter Client Email address if no Response from Agent after certain Wait-time
Let's assume that there are agents online and all of them are busy with current clients.
Then a new client starts chatting, however he does NOT receive any response although he waited a certain amount of time X.
After this X time has passed, display a custom message to the client, along with the possibility to enter his email address.
Custom message example: "All our agents are busy at the moment, however you can type in your email address below, and we will get back to your request as soon as possible."

Hi there Chris,
This can be done with Triggers. You can even customize the message a visitor receives.
You can read more about Triggers here https://www.tawk.to/knowledgebase/advanced-features/creating-and-managing-triggers/
The email is entered in the prechat form so you will be able to contact the customer through messaging section.
Hope this helps.
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Ken commented
Triggers would work, but we need the ability to bring up contact information similar to the offline message.
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Christian commented
Triggers: chat rescuer triggers will do that
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Chris commented
Related request: Display custom Message to Client if no Response from Agent after certain Wait-time - https://tawk.uservoice.com/forums/228427-feedback/suggestions/13596072-display-custom-message-to-client-if-no-response-fr