idlewatch should eventually watch the IMAP folder of your choice with the IDLE command and run a custom command when an event appears.

For the moment it scratches my itch: watching the "All Mail" folder of my GMail account, and run OfflineIMAP when a new mail appears.

Why

Polling sucks, and IDLE is the solution. I couldn't make OfflineIMAP's own IDLE work for various reasons, here's my attempt at making it work.

Installation

OfflineIMAP

First you need a proper installation of OfflineIMAP. Here's mine, elided with only the only important parts:

[general]
accounts = GMail

[Account GMail]
localrepository = GMailLocal
remoterepository = GMailRemote

[Repository GMailLocal]
type = Maildir
localfolders = ~/mails
folderfilter = lambda folder : folder not in [\
               "[Gmail].Important",\
               ]

nametrans = lambda folder : folder == 'archive' and '[Gmail]/All Mail' \
                         or folder == 'inbox' and 'INBOX' \
                         or folder == 'spam' and '[Gmail]/Spam' \
                         or folder == 'trash' and '[Gmail]/Trash' \
                         or folder == 'drafts' and '[Gmail]/Drafts' \
                         or folder == 'starred' and '[Gmail]/Starred' \
                         or folder == 'sent' and '[Gmail]/Sent Mail' \
                         or folder

[Repository GMailRemote]
type = Gmail
remoteuser = myuser
remotepass = mypassword
sslcacertfile = /etc/ssl/certs/ca-certificates.crt

nametrans = lambda folder : folder == '[Gmail]/All Mail' and 'archive' \
                         or folder == 'INBOX' and 'inbox' \
                         or folder == '[Gmail]/Spam' and 'spam' \
                         or folder == '[Gmail]/Trash' and 'trash' \
                         or folder == '[Gmail]/Drafts' and 'drafts' \
                         or folder == '[Gmail]/Starred' and 'starred' \
                         or folder == '[Gmail]/Sent Mail' and 'sent' \
                         or folder

You must have a [general] section, and the first of your accounts must be GMail.

If after that you can run

$ offlineimap

in your shell, you're good to go

idlewatch

• install the Go toolchain
• compile with

$ go build

• run it (preferably in the background, with a tmux or with a proper service management)

$ ./idlewatch