Chat trigger to tag a chat when a customer has initiated a chat with an agent, but then the customer doesn't respond and remains idle

We have spoken to Zendesk Support who has confirmed it is not currently possible to create a Chat trigger to tag a chat when a customer has initiated a chat with an agent, but then the customer doesn't respond and remains idle for a specific amount of time, or just idle. We would like to be able to tag these types of chats. Could you please confirm if this functionality will be made available in the future?

Secondly, we understand we may be able to use dropped chats instead - Dropped chats are the number of chats where the conversation with an agent ended with an unanswered message from a visitor. 

However, it doesn't look like dropped chats are tagged with a specific tag could someone please confirm? We can see missed chats are tagged with zopim_missed_chat.