How to Sync iphone contacts to gmail I have the old iphone 3GS
LATEST IOS

I used to open Itunes to put songs on the phone etc and if I wanted to I would (manually)sync my phone. Syncing the phone enacts whatever your options are set to. In my setup that meant, hitting "sync" would cause: 

1  Backup- iphone backed up to the PC,  

2  Calendar - iphone calendar synced with Oulook calendar on my computer

3  Contacts, that is the iphone contacts (phone nums, and any other info like street address, email address)  - synced with gmail contacts.
NOTE: In 2 &amp; 3 syncing meant that any new contacts put in the iphone since the last sync, would be added to my gmail contacts and any new contacts in my gmail contacts that were not in my iphone were added to the iphone. So the syncing worked both ways. Handy, as if I ever lost my phone (apart from having the backup on the PC) my phone contacts would be in my gmail. 

I did not do the above sync for some months and when I went to do it recently I find that Apple has changed things. The dropdown list that had gmail on it for selecting which email application you wanted your iphone contacts to sync to, no longer had gmail on it and it had to defaulted to Outlook. Certainly don't want contacts to go there.
So I unselected the contacts sync so now when I sync only my calendar gets done.

Apple apparently wants to be less connectable to non apple entities, so wants people to sync contacts with icloud. Useless for my purposes. :(

My question:
HOW TO sync, if possible, my iphone contacts with my gmail contacts even if it is a 2 step process. There are a lot of questions similar to this on the site but none seem to deal with the fact that I want to be sure that I do not cause any iphone contacts to be wiped in favour of what is in my gmail contacts or vice versa

( Back a few years, I thought I would make a new start with a clean slate on my gmail contacts so wiped them all and then synced, thinking all my iphone contacts would appear in my gmail contacts. Because the syncing process updates the other entity with the latest actions from and to each other, the iphone was updated by the latest actions which were in gmail contacts, so wiped the iphone contacts clean! 
Was not happy)

With all this in mind, can anyone tell me how to do a 2 way update (sync) or if this is no longer possible to at least update my gmail contacts with any changes in my iphone contacts?

HELP is appreciated.
All google syncing is done through the wireless connection now.  Go to the Settings app, and choose Mail, Contacts, Calendars.

Choose Add Account... and select Gmail from the list.  Follow the instructions to connect to your google account, and then select whether you want to sync more than your contacts.

Tested on my iPhone 3GS with iOS 6.1.3 (6.1.6 just updates a few security issues, no change to the contact/gmail sync)