Stock EMAIL app- Exchange updates fine. but GMAIL doesn't sync up?

[BacktoSmartPho]

on the stock email app, my Exchange account will allow for true email push, or will update every 15 minutes or w/e

my *gmail* acconts will NOT automatically check for mail, even when I have "check every 5 minutes" set in settings.

Now, please not that under my phone's general settings (Galaxy S3), I have DE-selected the option to sync all my accounts. Does this matter (kjust trying to save SOME data)?

 

[BacktoSmartPho]

I solved the problem. indeed, I needed to make sure my *gmail* accounts i the Sync (in settings tab) were all selected. There were redundant Google accounts there, as well, which I de-selected. Email now is forwarded every 5 minutes, as I hoped