Hello, I started working on a 1982 Datsun 280zx, and it runs, but the fuel injectors for cylinders 1 and 2 fire sporadically. First, neither of them worked. I replaced both injectors and that got 2 to pick up, but still nothing from 1 on a brand new injector. next I had to fix a spark issue, and now it seems like 1 is firing and 2 is dead. I've replaced both connectors and 2 is still not opening. Is there anything else I'm missing, or is this looking like a short in the wiring somewhere? God forbid the ECU itself is the problem. The previous owner said that one of the fuel lines connected to the injectors sprung a leak while it was running and started a fire under the hood. They replaced all the hoses and wires before they decided to sell it, so that could be a cause for a short. I'm mainly wondering if there's anything else I can check before I have to go digging through the ECU harness for a short. Thank you for your time, and I apologize if somebody else made a post like this.

(TL;DR all fuel injectors open on their own, but # 1 and 2 act weird when in car. Should I be looking for a short in the wiring harness?)

 

How are you determining that the injector(s) are not firing? The ECU grounds the injector to fire them. Check for 12 volts on one side of each of the injectors, but U must unplug all the injectors to check for +12. Wiggle the wire harness to see if voltage change while checking.
Most of the time this is a bad connection to the injector but since you replaced all(6) of the electrical connectors on all of the injectors this should not be an issue. The way the ECU fires the injectors is that the ECU counts how many times the ignition coil fires and every 3rd fire of the coil the ECU fires all the injectors at the same time (gang fire). You can check the ECU by using a ground wire to fire the coil without cranking the engine. Turn on the key and ground the neg side of the coil 3 time fast and see if the injectors fire. Are you using a noid light to check the injectors for firing?
Being that there was a under hood fire, I would look for poor splices under whatever the PO used to wrap the harness after repairs. You can pull the entire wire harness in about 20 minutes. Take pictures of the routing before you pull it if it comes to that.

1982 cars should not have a dropping resistor, but odd things happen when cars are built. Verify you do or don't have the dropping resistor. If you do, clean the connector on the resistor. The resistor would be located on the drivers side fender in front of the master cylinder beside/under the washer tank. If you don't have the resistor you can only use the 1982 and 1983 ECU.
You can see the dropping resistor here circled in red

 

I unplugged the injectors while the car was running to check for a difference in the engine sound, and there was no response for 1 and 2 at first. I swapped the injectors and 2 started working, I changed the connector for #1 and still no response. Then the distributor rotor went out, so I swapped that, the cap, the plugs and the wires. After that 1 started working, and there's no response when I unplug 2. I'm at work now so I haven't had a chance to check with a voltmeter. As of now, I've only replaced the connectors for 1 and 2

 

There were a couple of bad wire splices under the harness for the injectors what were giving me trouble. All it took were some new butt connectors, and now it's firing on all 6. Thanks for your advice kickstand

 

I am happy to help. Now go drive your Z!