First step if i was you would be to create a Custom Bot, from "new conversations" in this bot you want to give the customer a few options to choose.

Important here is to "disable the composer", which means the client can't run a message but is forced to have make a choice.

That helps you sort the customers by their issue without having conversations that are not clearly routed

Based on the customers answers in this bot you can route it to specific teams using rules or in the creation of the Bot.

From this point on you can't send automatic replies as a person, but a workaround would be to either customize your bot by making it more individual. Instead of bot, you could for example call it "Marie" or "Viktor"

Personally I prefer letting the client know what is a robot and when I'm online.

A good solution for that would be using the "chats" feature if you have a dedicated URL for you support page.

If you have a www.example.com/support you could have these kinds of messages appearing

Which could be classed as "trying to contact support"

As of know as far as I know we do not have the option to automate messages from personal Intercom accounts.

But these options give you more possibilities in creating your support experience.

Hope this helps somehow.

//Viktor