I would remove both, charged them independently of each other, than have then load tested by a battery store.
How old are these batteries? You might find in the long run its better to just replace the pair.
That rotten egg smell is caused by the sulfuric acid in the battery boiling. Its also releasing hydrogen gas which is explosive.
Yes ago when I was an Mechanic apprentice my boss pulled me over to show me how to charge a totally dead battery using a 2nd good battery that would excite the charger so it would turn on. He pulled the charger cable off a battery and the spark blew up the battery in his face. My job was to hose him down to get the acid off his face. There was plastic stuck 12' up in the drywall. I will never forget that demonstration