I guess like any deer we'd immediately recognise (and love) the taste of rock salt
Regular mineral water will avoid that.
Mineral water may have a small amount of trace minerals, but it has basically zero electrolytes at relevant physiologic concentrations. Functionally, there'd be almost no difference between distilled and mineral water fasting with respect to electrolyte management.
Imbalances in sodium, potassium, magnesium and calcium can get VERY serious very quickly. Mineral water does not really have relevant concentrations of those.
I think you're conflating the idea that distilled water isn't particularly good for you since it starts leaching out the trace minerals from parts of your body, with the entire concept of electrolyte management. These are VERY different things, occurring with VERY different relevant concentrations... like at least 1-2 orders of magnitude.
This might be correct for what is considered mineralwater in the US (I honestly don't know), but 1l of typical sparkling mineralwater in Germany has about a third of your daily magnesium and calcium recommended amounts (as well as relevant amounts of a view others). https://www.gerolsteiner.de/wissensquellen/wasserwissen/mine...
And there are waters with even higher concentrations.
The GGP mentioned "regular mineral water" - but most of us (at least in the US) do not purchase bottled mineral water to drink on a day-to-day basis. Most of our water consumption, in one way or another, comes out of the tap.
And for Na the recommended ammount is 1.5 g (from D-A-CH)
But in the example linked above, 1 l of the water gives 118 mg of Na, so 13 l of water would be needed to get the required Na amount. Not practical, but most mineral waters actually come rather with an artifically reduced amount of Na. Natural sources probably have higher values.
But in
https://www.dge.de/presse/meldungen/2011-2018/aktualisierte-...
The US FDA says 2300 g max.
https://www.fda.gov/food/nutrition-education-resources-mater...
Depends on the water. All the water sold or the one from the tap is artifically reduced in Na.
A natural spring might not be and has high values. Or a well in the desert (they can be very salty).