Enable Queue keeps all the incoming chat requests on hold if no qualified agents are available to accept the requests i.e if all the agents are at capacity. Currently, there is no configuration available to auto end or notify the customer via the chat in specific time.

 

 

Currently, this is not available. Please vote for the idea:
https://ideas.salesforce.com/s/idea/a0B8W00000GdX0sUAF/live-agent-more-control-over-chat-request-timeout-configuration