Mailserver push to gmail

I have a local mail server, running on my own custom domain.

I have set it up as an alias in my gmail account, and use gmail to send and receive emails via said server instead of logging into it directly.

It works well.

The only real downfall is that gmail only checks POP every hour or so. Ideally I’d like this to be a little more responsive.

Is there an API I can hit that informs gmail that a new message is available on my mailserver, and it should run a POP job now? My basic idea of the workflow would be as follows;

  1. I receive a message on my mailserver.
  2. This triggers a script which can do whatever is required. Ideally in a non-evil way.
  3. The result of step 2 is gmail knowing that it needs to do a POP update, either for the account or more ideally the single relevant address.

Is there a way to pull this off? For bonus points, can it be done in a such a way that avoids me needing to know gmail credentials – as then I could use the same method to quickly update client’s inboxes as well.