TOPIC:

Ok, here we go. Background. This bike has been fighting me every step of the way.  After reading on this forum some time back about how the stock coil/resistor setup was weak and troublesome, I upgraded to Accel coils and wires. they worked fine. I went to start it one day and no spark. Assuming the new coil setup blew the old CDI, I replaced it with a new Carmo unit. Still no spark. I checked all connections and a friend helped me check continuity and ohm out everything. there is power from the small connector to the CDI. there is power from the CDI to the coils. the only thing we couldn't check were the pickup coils. They don't match what is in the shop manual, including the wire colors. so now I'm stumped.  While I'm waiting input from the pool of 1300 geniuses here, I'm also going to go through every electrical connector, stem to stern and make sure they're clean and tight. The pictures show the pick up coil setup I have.  Additionally, the old CDI isn't even stock.  I'm wide open for ideas.

 

There's a lot to digest here since it's a non stock setup so I'll just throw out some thoughts as they come to me.
First, you note that the wiring doesn't match the wiring diagram. You're working on the 1981 A3 model so you should be following the wiring diagram for the A3 in the supplement for the A3. Wiring diagrams for the 3   A3 models start on page 333 in the manual and all 3 wiring diagrams show 5 wires - red, white, orange, gray and brown coming from the pulse coils. 
Second- The ignition on the A3 (1981) is completely different than all other models, so when trouble shooting you need to follow the supplemental section  for the A3 starting on page 322 in the manual.
Third, one of the unique things with the A3 ignition circuit is that when you turn on the ignition and before cranking, the IC unit starts a timer circuit and if the timer set point is reached before cranking, the IC turns off the power to the coils to save battery voltage. Then the timer circuit waits to see pulses from the pulser coils and when it does, it turns the power back on to the ignition coils. if it doesn't see the pulse, it won't turn the power back on.
Fourth, you mentioned the weak ignition system reported with the stock coil set up. If I've learned anything over the years about information on the net, EVERYTHING talked about needs to be taken with a grain of salt. When you start changing out parts and don't maintain the same standards parts for parts, you introduce new problems. Ignition coils with lower primary ohms will produce a hotter spark but the lower ohm resistance of the primary allow more amps to flow in the primary circuit and the switches (transistors) in the primary circuit need to be able to handle the higher flow of current. The stock Igniters can't handle ignition coils with primary circuit ohms of 3 or less. 
We have heard about the Carmo units a couple of times on this site but there's little knowledge regarding the units. I do know that camo produces a unit for the 1979-80 and a separate one for the 1981. Unless the Accel coils fried the transistors in the Carmo unit I doubt the camo unit is the issue. Whatever happened here happened overnight and if the coils fried the transistors, it would have happened one at a time, not all at once.
Pick Up Assembly Inspection page 330 in the manual. Because it ran the night before and won't start the next day, I suspect it's something simple. Either the timer circuit in the IC unit is not sensing the pulser coil pulses and turning back on the power to the coils, or heaven forbid, the engine kill switch is faulty and that circuit needs to be checked. Never overlook the most simple issues. Lots of people assume the worst and dive deep in to the guts of a system only to find out in the end it was something as stupid as a blown fuse or a bad switch on the handlebar that got soaked with rain and decided to ground out. 
Hopefully, some of these ramblings help provoke some thoughts. Let us know how your making out and what you find. It might trigger more thoughts so we can help
KB

Thanks, Kawboy,  I'll check all this out and let you know!

Apparently I have a, different manual. It only goes up to page 300. The wiring diagrams only cover A2 and B2. I have the red cover service manual. 
The white mantel appears to cover the A3, and I've just ordered it from Ebay.  Thanks again,  KW.

81Barnfind- The Service manual you need is available for download from the Home Page on this site. IT"S FREE for the members !! 3rd manual down. (near the bottom of the page)

Good to know. Thanks,  that'll let me get started. Being an old fashioned guy, I like a paper manual,  so no harm.