As an aside......
I always disconnect my battery negative terminal (terminal easiest to get at with 8mm flex open end ratchet) when I expect to not drive the Z for over a few days (say a week). Even when sitting for several months with battery disconnected, the engine fires right up after reconnecting the battery.
The batteries just do NOT discharge significantly by themselves even over a several month period when disconnected.
This applies to my tractors, lawnmowers, ATVs, trucks, cars.....everything with a 12 volt battery. Obviously I have to reset those items where memory is lost by the battery disconnect which are very few (clock and radio selection). I used to mess around with Tenders but got tired of having to leave electricity on just for a tender.
I am a minority in this regard on this Forum (actually prolly the only one) just so you know
I do this only when the Two Zs (LT5s) and 90' (L98), Tractor, lawnmowers, ATVs, trucks, cars are sitting for a week or so.
IN several years with doing this (three trucks including a Tacoma, two JD tractors, three Craftsman Lawnmowers, Two Yamaya ATVs, One Polaris ATV, several cars including a 90' Z, 91' Z, 90' L98)
leaving battery disconnected for short and long periods of time in temperatures 70 deg to zero.....
every single one has started right up when battery was reconnected
The only item I have to reset on the Z (LT5) and L98 was the radio selection
Those are the FACTS and others can talk but without facts
And it does NOT make any difference on which post I disconnect (on the Corvettes I disconnect the negative post since it is closest to my 8mm open end ratchet wrench)
Also....it IS excellent practice to disconnect the battery when working on the engine as no one can disagree there except some maybe that disagree with ALL my posts
I do not disconnect the batteries on anything I might use within a week. I have had some tractors and Corvettes sit for two or even three weeks with battery connected occasionally without a starting issue. But in general I have always had problems with batteries connected for long periods of time and the worst thing you can do is let a battery discharge for long periods of time. So...in general this is what I do.
Oh....and I do my own modifications and maintenance on ALL vehicles with the ATVs and Corvettes heavily modified and ALL runing perfectly.
I will go out and hook up a battery with 11.5 volts and see if the Solenoid does its job and report back.....I have some of those batteries sitting on the shelf as I have to replace say a battery every 3 years having 15 vehicles with batteries.
Bottom line...you have an opportunity to try something I did not try when this happened to me.....connect 12.7 volts to the purple wire and main starter cable (assuming both cable ends have good contact with Starter).