Electrolytes are generally OK during a fast. But be careful not to stimlate the excretion of minerals by taking too much: The quickest route to a deficiency is often a supplement: Supplements are absorbed so fast, that their blood levels rise very quickly, causing the elimination mechanisms to be triggered. This elimination then continues after the absorption is completed; you may thus lose more than what you took. That's one reason only drug addicts need drugs to function.
There are many electrolytes in the body and many of them cannot be measured accurately as they are intra-cellular. Sure if you can have the most important ones (Sodium, Potassium, Phosphorus, Calcium, Magnesium, Bicarbonate and Chloride) checked by a reputable laboratory, that will help safeguard you at least insofar as those are concerned.
Our normal electrolytes comes from food. In the food they are typically associated with organic molecules and they are distributed throughout other substances. Thus they get released for absorption over several hours at least, as the whole "bundle" moves through the intestine.
A "supplement" is highly concentrated, so as it strikes the stomach, the acid there would release the minerals, ready for absorption. The whole lot would typically enter the bloodstream within minutes. Now our natural homeostatic mechanisms "estimate" the volume of mineral "on its way" by evaluating how much arrived in say the first half hour, then "calculate" from that how much to expect over the next few hours.
So if your body "expects" a huge load (based on the volume arriving in the first few minutes) it would need to prevent toxicity by activating the elimination of these minerals in anticipation. This elimination "picks up momentum" which is continued long after the (rapid) absorption is completed. This is the same mechanism by which "vitamin supplements" causes a vitamin deficiency and by which drug addicts would get overtly ill when they stop taking drugs.
The minerals I do allow to enter my system during the fast are those in a good mineral water, preferably of Dolomitic origin (Although most of my fasts are dry). I don't "take minerals" any other way during a fast. If you do, that would not terminate the fasting metabolism as there are no energy-containing nutrients or taste associated with them. Bear in mind that if you measure blood minerals (in particular Magnesium but also Calcium) you measure them in a location where a VERY small percentage of the mineral is located. Thus it does NOT reflect the levels in your body as a whole.
I would never suggest taking calcium without magnesium or vice versa. A very low dosage would likely suffice but once again, if it is highly absorbably (as with fizzy electrolyte tablets) the excretion may be triggered. Thus I only recommend Dolomite (the natural source of calcium and magnesium in the correct ratio) for those who need it. It has the added benefit of neutralizing excess stomach acid which is sometimes present in novice fasters.