Can you exclude your private ssh key from being synced with google?

Why do you think the private ssh key would be sync'd with Google in first place?

There's no background sync of your Android phone's contents to Google, just things like Contacts and Email (which are optional)

When I setup an Android phone I am asked if I want to sink my configuration and data with Google, and that this information includes things like wifi psks.

Are ssh keys stored in an area that is separate from what Google syncs?

As I understand it, it's up to each app to decide what exactly it will back up. After a quick glance at the code, it seems to me that it backs up preferences, host keys, and public/private keys.

Okay, so that's a big red flag for me. Google can't have my private keys, so I can't use it. Thanks.

Of course, you could download the source, comment out the lines that do that, and use the app. Or just don't enable the 'backup to Google' option.

Yep, I could do, but that's too much work.

I want backup to Google, for everything apart from that.