Well, now we’re getting outside my field of expertise, so all I can do is make some general remarks.
The zinc gluconate may be neutral, but I can not tell what effects (in the sense of: chemical reactions) the zinc will have once it’s inside the stomach. It might undergo some reaction which either increases or decreases the acidity of its environment, or it might have no effect at all on the acidity.
(As you see, there are lots of “may” and “might” in my wording. I’m really merely “thinking aloud”, so please view my remarks as thoughts, not as statements.)
I guess, however, that the above effects do not really count even if they do occur, because the amount of zinc is too low to have a noticeable effect on acidity through these mechanisms.
A wholly different effect may occur if the zinc binds to the stomach’s acidity receptors, or even poisons them. That may cause the stomach’s acidity regulation system to not function normally. I really cannot tell if this is possible at all.
Sorry I can only provide some thoughts. I don’t want to pretend I’m sure when I’m not, so I openly share all doubts and disclaimers that apply.