Many `POP3` servers "discourage" too frequent polling.

https://webmasters.stackexchange.com/questions/49721/what-is-the-maximum-frequency-for-checking-email-in-gmail-and-are-there-alterna

Use `IMAP` with `IDLE` command instead of `POP3`.

Both `fetchmail` (program) and `gmail` (email provider) support IMAP with IDLE.

It would require one fetchmail process per one monitored IMAP account. 
`fetchamil` will keep one IMAP session open permanently. 
You should get "near real time" notifications about new emails.

`man fetchmail` 
> --idle (since 6.3.3) 
(Keyword: idle, since before 6.0.0) 
Enable IDLE use (effective only with IMAP). Note that this works with only one folder at a given time. While the idle rcfile keyword had been supported for a long time, the --idle command-line option was added in version 6.3.3. IDLE use means that fetchmail tells the IMAP server to send notice of new messages, **so they can be retrieved sooner than would be possible with regular polls**.