I only saw option to sync at intervals.
Settings/Account settings/the account/Sync settings/Sync schedule/Set sync schedule. The first option should be Automatic (Push).
I had it working one of my accounts today and checked battery and it said the email app had used 8%. Not sure I liked that.
That's 8% of the amount of battery that had been used, not 8% of the battery capacity. If all the apps that used any battery since the last charge were shown, the numbers would
always add up to 100% - 100% of the amount of battery being used is being used. That could be 1% of the battery capacity, or it could be 99% of the battery capacity. GSam shows that Email used 1.4% over the last 4 days. And I get a lot of "X posted Y on Facebook" and "Free offer at xyz" emails. Four accounts on the app. The 5th one is something I only use for stuff on the desktop and the 6th one has turned into a garbage dump, so I glance at it every few days, check all, uncheck 1 or 2 that are real emails, delete and archive what's left - on the desktop.)