The acid pretty much stays in the lead plates.
Hmmm, I always thought the acid is in the electrolyte. Except what comes out the vents causing corrosion.
I find the battery oil is interesting. Here is a little history I found on the web;
Edison sold his Nickel/Iron battery to the Telephone , Telegraph, Railroads , and for early penny in the slot amusement listening tube phonograph use.
The Telephone & Telegraph companys had iron battery boxes on their poles with banks of the Edison Nickel/Iron battery in them.
The railroads had iron signal boxes which also contained banks of Edison batteries.
The "Battery Oil" was poured on top of the fresh electrolyte in each cell to prevent evaporation and gassing while charging on these utility poles. The oil would float on top of the electrolyte to give a thick protective oil film.
This would help the battery gases to re-combine instead of gassing-off while sitting long term, or re-charging. It also prevented evaporation.
You often find empty Edison Battery Oil bottles of 3-4 oz near old railroad iron signal & switch boxes in the woods near the switch & signal boxes today.
You often find old Edison battery jars on eBay !