2 brought quotes from linked article inline (it's been two months, OP is not going to do so even though comments asked for this)
source | link

This might the solution you are looking for: http://www.neowin.net/news/how-to-use-google-services-in-windows-phone-8

Check the section Push Gmail and syncing contactsPush Gmail and syncing contacts:

While there is an easy option to simply sync your account as a Google account in the settings, you'll get better results if you set it up as an Exchange ActiveSync account because it enables push email. Don't worry, because all of your contacts and your primary calendar will be synced across as well, just like if you were to set it up as a standard Google account.

. . .

To set up said Exchange ActiveSync account, go to the phone settings and then to email+accounts > add an account > Advanced Setup. In this menu, enter your Google account's email address and password, click next and then choose Exchange ActiveSync. From this menu with more options, the necessary Server box appears; here enter m.google.com, click sign in and you're all good to go (leave the Domain box blank).

Screenshots and more details at the linked article.

This might the solution you are looking for: http://www.neowin.net/news/how-to-use-google-services-in-windows-phone-8

Check the section Push Gmail and syncing contacts

This might the solution you are looking for: http://www.neowin.net/news/how-to-use-google-services-in-windows-phone-8

Check the section Push Gmail and syncing contacts:

While there is an easy option to simply sync your account as a Google account in the settings, you'll get better results if you set it up as an Exchange ActiveSync account because it enables push email. Don't worry, because all of your contacts and your primary calendar will be synced across as well, just like if you were to set it up as a standard Google account.

. . .

To set up said Exchange ActiveSync account, go to the phone settings and then to email+accounts > add an account > Advanced Setup. In this menu, enter your Google account's email address and password, click next and then choose Exchange ActiveSync. From this menu with more options, the necessary Server box appears; here enter m.google.com, click sign in and you're all good to go (leave the Domain box blank).

Screenshots and more details at the linked article.

1
source | link

This might the solution you are looking for: http://www.neowin.net/news/how-to-use-google-services-in-windows-phone-8

Check the section Push Gmail and syncing contacts