So I've been having this issue with my 97 z28, usually only when warmed up but not always, where sometimes it won't start, at first it would just click rapidly like a starter issue but would still start after a few tries, then the next day it became a single click and the lights would flash on my dashboard like its a battery issue, then now it's like flashing the dashboard lights for a split second and then they turn off, the only way the car will start now is if I turn the key to on in the split second that the lights come on? I don't think it's the battery because my battery has good charge after I tested it, so what else could it be? I just had the ignition switch replaced about 3 days ago so I don't think its that either

 

clean all cable connections at the battery, inspect cable ends to ensure the wire is getting good connection to the cable end fitting, over time the wire can build up carbon and cause a connection to fail partly enough to possibly cause what you are seeing. there are two junction boxes one, positive is red other has no color or cover and is ground, take wires off and clean wire end connectors. I would consider new battery cables if they look questionable

 

What Craby said and if you still have the problem take the battery to get load tested.