jjpal,I'm glad to hear the problem has been isolated and I will answer the questions of why and what,but first I'd like to say something on behalf of those who replied on this. Thank you for letting us know how this turned out. I can't tell you how important it is for us to hear whether our advice only got someone in more trouble than they already had or if it actually helped them. We don't need a pat on the head,we just need to know when advice was understood or was ambiguous.
As for your question of how or why voltage was fluctuating for no apparent reason. Electric current doesn't have moody days or wild notions,it behave's in a predictable way EVERY day,EVERY time. When it suprises us,we need only to take the knowns about the circuit and run simple tests to find what is amiss. E-V-E-R time we try discussing a problem with lights,ignition,battery or starter,some smart *** attempt's to lead us into AC current and/or electronics. That is nothing but strutting and preening to show what they know. I will say here and now,understanding DC current is all one need's to work on tractors,trucks,cars,motorcycles and for the most part,home appliances and wireing. It is with that understanding,we talk about the inconsistent voltage you observed. If you follow both wires from solenoid back to - & + battery posts,odds are 99% you find loose conection,corrosion between connection or broken wire making intermitting connection(likely with corrosion at break). Following - back to - battery post often lead's to a connection to frame or engine block. Just test that connection and battery cable connection to frame and battery post. Keep in mind all those can and do occur INSIDE switches as often as at mechanical connections. In this case,the fault is in + wire but the effect is the same on -side. If you are not content using the newly installed switch,here's tips that might help locate fault. First suspect is ignition switch. Make sure connections are clean and tight. See if wire is broken inside jacket. To test guts in switch,hook one lead of volt meter to ground and other lead to terminal feeding solenoid. Run engine using new wire and switch while watching for volt variance on meter. Hopefully what you experienced with this help's with future electric grimlins.