Paddle,
I can't answer your question. There are a lot of variables to consider.
My guess is that allowing additional atmospheric oxygen into the jar will contribute to the formation of iron oxides. But remember that these acid/iron stains work but carrying iron ions into the wood as part of an iron/acid salt solution. The vinegar/iron stain uses iron acetate to carry iron ions into the wood. The aquafortis (nitric acid/iron) stain uses iron nitrate to carry iron ions into the wood. Then, when the acid evaporates out of the wood the iron ions acquire oxygen from the air and turn into ferric oxide.
Iron oxides, FeO and Fe2O3 are slightly soluble in acids. So you might get some brown color from the solution. But be careful, that brown color can be suspended iron oxide. That suspended particulate will not give you the depth of color and chatoyance of a true acid/iron stain. I alowas decant a clear solution off my acid/iron stain crock and use that as the stain.
Best Regards,
JMC