Thanks to all who have given suggestions, I really appreciate the help. I have been working on various cars and motorcycles for over 50 years and this really has me going a little nuts.
A little more background. This car sat for several years with the blown headgasket. It started right up with a little boost to the battery. But the fuel pump eventually gave out from our friendly ethanol gas corrosion fun. So I installed a new fuel pump. It is working fine as I ran it to empty the fuel tank and develops good pressure. The tank now has about 10 gallons of fresh non-ethanol gas which I keep on hand for my old Honda Goldwing.
After pulling the engine to look at a rebuild I noticed 2 egg shaped cylinders which meant a full rebuild not just head gaskets so I bought a used JDM engine which is what I am trying to make run now. Point of interest: I had moved the car around with the original engine on my property several times before I pulled the engine. I noticed that each time I started it up and moved it, the engine was a little harder to start, doing something similar to what it is doing now, but it always started and seemed to idle and rev smoothly. Maybe it means nothing, I don't know.
If I haven't already stated it, the current engine turns over briskly and fires #1 and #2 and outruns the starter sometimes, but just won't fully run because I get no spark to the other 2 cylinders. Fuel is clearly getting to the injectors. The problem is no attempt to fire the second half of the coil.
Now to the suggestions:
I have carefully examined both sprockets (from the original engine and the swapped in one) and they appear to be identical in every way. Though I have no precision tools to measure the angles of the magnets (and they are magnets on both sprockets) with respect to the alignment pin between the sprocket and the cam, they appear identical.
I do not have an automotive scope so I can not take a look at the waveform coming out of the sensor, however, since I get a steady signal out of the ECU for cylinders 1 & 2, it appears that the info from the cam sprocket sensor is getting to the ECU.
I have checked the sensor and wiring and all appears well. If I pull the connector off the cam sensor I get a Code P0340. When I replace the connector, clear the code and crank again the code does not re-enter. The same is true of the crank sensor which returns a P0335 code when disconnected.
So, in summary: Both sides of the coil check out OK as I can make them both fire by hooking the Cyl 1/2 lead from the ECU to the ignitor to the Cyl 3/4 ignitor input. This also verifies that the ignitor is working on both sides. (I did this test with the plugs removed and grounded so as not to fire #3 and #4 ad in appropriate times with any residual gas in the cylinders).
The wire from the terminal pin on the ECU to the ignitor checks out in a resistance test ok and is not shorted to ground (or power for that matter). A close inspection of the terminals on the connector and the ECU appear in good working order.
I have swapped the ECU with a used one with the same result. I suppose it is possible that the used one has the same failure, whatever that is. A new one runs between $700 and $1000. I can not seem to find any place to test the ECU. The Subaru shop manager all but laughed at the request saying that none of the systems can be checked out of the car and it must be brought in to troubleshoot it. Sounds like a new car would end up a cheaper deal.
Since I don't know how the firmware in the ECU works and it shows no codes when the sensors are connected, I can't figure out why the ECU would fire #1 and #2 but won't attempt fire #3 and #4.
As an after thought, I should mention that I have not put the radiator back in yet as I was concerned that I may have to re-do the timing belt, so there is no coolant in any part of the engine. Is it possible that it requires some coolant sensor to detect fliud to run? And if so, why would it fire any spark plugs at all? The air sensors are hooked up and everything else that I can think of (or find) is connected.
(looks like I wrote a novel)