Automatically check one account but not another?

I have two accounts, both are IMAP. I want it to automatically check messages in one account, but not the other; I just want it to check/sync the other when I open that folder. Is this possible? I did take the check out of “Include this account when sending/receiving email” in the accounts settings, but it didn’t seem to make a difference.

Most of the IMAP servers supports IDLE connection which makes this impossible. The only thing I can recommend is using POP3 protocol instead of IMAP.