Before we start changing batteries, or even installing the auxiliary relay (never a bad idea, tho), Some basic troubleshooting is called for.
Check battery voltage. Fully charged it should read ~ 12.6 VDC at rest (!14.7 when being charged).
The two most common "NO START" issues on the 90-92s are either the clutch safety switch or the solenoid contacts within the starter itself. And, a third relay is commonly known as the VATS relay (but unless your security light is flashing when you turn the ignition switch to START, that is not likely the issue).
Use the schematic provided that was published by Marc Haibeck that provides common voltages along the circuit WHEN THE IGNITION SWITCH IS IN THE
START position.
IF the purple wire between the clutch safety switch and the starter has voltage on it when the ignition switch is in the START position, then chances are the starter solenoid contacts need replacement (will cost you about $10-15 for the Denso Starter Solenoid kit (See
Jerry's Gaskets for that or whatever else your LT5 needs, including plenum gaskets you will need when you pull the plenum - a "rite of passage" for all ZR-1 owners!). Also, Most auto parts stores have the kits. Many domestic and foreign cars use that Denso starter(s).
Well, I don't want to jump ahead too far. But, refer to the schematic and use your VOM and trace the voltage from the battery to the point where you loose it. That will be the location of the fault.
The BIGGER POINT I'm trying to make is, before you start changing parts, VERIFY that the fault FIRST! Otherwise you'll be headed for a lot of frustration AND expense TOO!