Go to Settings > Channels > Messenger click into the Web tab, then click into the Show the Messenger Launcher section and toggle off the option to show the Messenger launcher for Users or Visitors:

This will hide the Messenger Launcher on Web which also prevents customers starting a conversation or seeing past conversations in the Messenger.

Your Messenger visibility settings will also apply to the Messenger on your Help Center. If you don't want to hide the launcher on your Help Center, add the display condition "Current page URL contains [your help center domain]".

If you want to hide the Messenger programmatically, you can do this by adding the key-value pair hide_default_launcher to true or false in your intercomSettings snippet.

Or, you can control which types of visitors and users can see the Messenger on your website.

All your Proactive support in-app messages are still delivered to your users even when the Messenger Launcher is hidden.

Your users will see these messages and can engage in conversation with you, but as soon as they've read or dismissed them, they won't be visible to the user anymore. 

These will be available to view if the launcher is turned back on.

There isn't a preset way to specifically hide the Messenger based on your office hours or for specific hours.

That being said, you could use a custom code on your website to show/hide the Messenger depending on what time of day it is, using the hide_default_launcher attribute in your Messenger installation code.

If you want to completely disable the Messenger and all Intercom features outside of working hours, you'll need to use custom coding to only install and boot up the Messenger during working hours, e.g. if working hours = true, boot up the Messenger. If working hours = false, don't boot up the Messenger.
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If Workflows are part of your subscription, you could also have a bot-only experience outside of your office hours instead of hiding the Messenger.

You can also hide the Messenger launcher in your mobile app. Here's how: