I can see the Baking Soda (it's alkaline--should neutralize acid), but Vinegar or citrus? Those are, themselves, acidic in nature.
Maybe a little distilled water with the Baking Soda to make a paste and then gently clean it (light scrub) with a soft, soft toothbrush.
NiCad batteries contain acid?
Nickel Hydroxide plate, cadmium electrode and alkaline electrode. Not sure what's doing the oozing but it's obviously corrosive (oxidizes.) i'm not sure there's anything in there that's an acid though.
But baking soda is a great cleaner for acids or bases in any case and it doesn't stink.
As long as you remove any residue. Your teeth are a good example of how good it is.
@Zipper. My experience with A2000s has taught me that sometimes 3v just aint enough. But I'd check the RTC chip with a volt meter to see what voltage is getting to it from the battery. As it might be the battery, socket, bad solder joint, bad track, or a partial short that is causing the problem.