NewZed

Which relay did you use, 77 or 83? They're different. The test procedure for the relays is shown, with pictures, in the Engine Fuel chapter, or the EFEC chapter. Probably easiest to put a meter on the fuel pump leads and see if there's power when the key is turned to Start. You'll probably see power and can move on to some other possible source. Listen for pump noise. Disconnect the starter solenoid so it will be quiet.

You haven't said what year car you're working with. The relays changed over the years.

Is it a 1982 Ford F150?

Pretty sure he just calls out the wire colors. Here's a few, plus the Google search terms. Might be enough in here. https://www.google.com/search?q=site:hybridz.org+cgsheen+280zx+distibutor+wire&ei=3ebBWbDJNNTIjwO8qak4&start=10&sa=N&biw=1230&bih=881

He hasn't been on for over three years. cgsheen has posted a few times about which wire goes where. Tell people what you're actually working with first though, it's not clear.

Who rebuilt it? What was done? Receipts?

That's often a sign of a dead battery or dirty battery cable connections. You should be more descriptive than "clicks then stops".

That's normal, a long and a short. Although, with the VLSD diffs, the long one is a lot longer. Can't remember the actual measurements. Better check, the parts stores have been known to sell the wrong shafts. 300ZX's came with VLSD's in later years. Edit - just remembered that the VLSD's came with a different spline count also. Count your splines.

Download the 1980 EFI manual and run the tests for 1979. It has tests for all EFI engines up to 1980. This will tell you if all of the critical parts are connected properly. Seems like your coolant temperature sensor might be disconnected. http://www.xenonzcar.com/s130/other.php If you get some parts showing as incorrect, use the FSM to find out where they are and how they should be connected. Engine Fuel chapter. http://www.nicoclub.com/FSM/280z/1979/

The 280ZX starters are gear reduction. Not a major reduction like the race engine types. That would be the simplest upgrade. Lighter and more effective. Actually, if you ask for a 75 280Z starter at a parts store you might get a ZX starter anyway. SKU consolidation.

Don't be offended. Just get some numbers and post them. Aaaallll of the new to engines people do the exact same thing. They don't realize how valuable numbers are. Read through the Service Manual and you'll see that most of the operations/actions/fixes have numbers associated. For example - if the gauge reads 200 at max, you're probably okay. If it went to 240, you're probably not. No matter where you go you'll still be the same guy you are now anyway. Might as well stick around.

"Crank" means to spin. From the old days when they applied an actual handle to the crank shaft. Then spun it. If it won't crank that means that the starter solenoid is not getting power, or the starter is no good. Did you actually mean "fire"? Fire is when the spark causes the fuel-air mixture to burn. If it won't fire, that could be a spark problem or a fuel problem.

Overheating is a very basic fundamental car thing. You're in kind of a dangerous spot, with not understanding much about engine basics. You can waste a lot of money. And your problem could be more complex. When these engines overheat the cylinder heads tend to warp, sometimes taking a permanent bend. When they warp, the head gaskets fail. Then a steady cycle of overheating happens, similar to what you're seeing. The first thing to do if you see overheating is to check the coolant level in the radiator, and the overflow bottle. Have you looked at the spark plugs? They can offer a clue about bad head gaskets. Overall though, just make detailed observations, write down numbers if you can get them, then write well when you post. Actual temperatures that you see on the gauge would be a start. Actual RPM numbers. Times, in minutes or hours. Things like that.

This sounds more like a basic overheating problem. Temperature will increase slightly on the gauge while the car sits because there's no coolant moving past the gauge sender. But as soon as the engine starts the needle should drop. You either have a coolant flow blockage or a bad water pump or poor air flow. Heat soak is mostly just a "20 minute sitting" problem. If you start the engine before 20 minutes you're usually fine, or after about 30. But once you're up and moving the heat soak problem goes away. You're not describing heat soak.

neverdone asked a good question then. "Heat soak" typically refers to the problem where the engine, after sitting hot for about 20 minutes, like on a short shopping trip, will start but run like crap for about a minute, before clearing up. That's the problem I thought you were referring to. A Pallnet rail is probably not going to help your problem. Your description is still a little odd though, you're talking about the engine being off and driving the car at higher RPM in the same sentence, followed by the engine coming to a complete halt, which wouldn't involve higher RPM. Three things that can't happen at the same time. Maybe break the problem down in to a short time sequence, from when it runs well to when it doesn't. Is it a manual or an automatic?