Thanks to Erle, Hib, Ed, James, and even Bruce, I've figured out how to read Diagnostic Trouble Codes on the 1994-95 MY ZR-1.
The 1994 service manual is confusing on this issue. It says you cannot read the codes on cars with the 16 pin connector under the dashboard right above the pedals. The reason for this is because the 94-95 LT1 cars were wired up for OBD II, which was required in 1996. Since the LT5 was going to be discontinued after MY1995, there was no OBD II implemented on the LT5, but it got the 16 pin connector anyway.
I was able to read the codes on my 94 ZR-1 by grounding the #6 pin by connecting it to the #5 pin. If you look at the connector, it is trapezoidal in shape. The wide part is the top, the narrow part the bottom. The pin on the top left is #1, the top right is #8.
It's simple enough to use an unfolded paper clip to make the connection. Having done the above, turn the ignition key to the "on" position, but do not start the engine. Every relay on the car comes on (except the fuel pumps), so don't be alarmed if you've never done this. The "Service Engine Soon" light will flash a code 12 three times. It will flash once, then pause, then flash twice, then a long pause, then repeats two more times. Code 12 indicates everything is working. After the code 12 flashes three times, the SES light will flash out any DTCs that have been set three times each, starting with the highest numerically. If the SES flashes four times, then pauses, then flashes five times, then it's DTC 45. Follow the service manual for diagnosis and corrective action. Disclaimer: I provide the above information to save any 94-95 owners some time figuring out how to read DTCs on their ZR-1s. Use the information at your own risk. If you're not comfortable with that, please take your car to a qualified technician.