CB350 only firing on one cylinder

Hi all - as the title suggests, my CB350 is only firing on its left cylinder. Pertinent details:
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[*]It is a rebuilt engine and was started for the first time
[*]I am running a Pamco electronic ignition
[*]I used a timing light, and the left cylinder (the working one) is a little advanced, and the right cylinder (non working) is right on
[*]I am getting fuel as it is coming out of the RH exhaust
[*]When i manually open the throttle on only the RH carb, nothing happens (duh)
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Here are my thoughts/questions and some next steps I may take:
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[*]The strobing timing light (with inductive pickup) clearly senses a signal to the RH spark plug because it lights up, but could there be a scenario where the plug is getting electricity but isn't sparking?
[*]Could the fuel/air mixture be too rich? Sometimes when i turn the choke off, the revs climb without any input to the throttle. I usually freak out and immediately turn the engine off, but now i'm wondering if that was when the RH cylinder was actually firing. I've adjusted the fuel/air mixture screws on both carbs around the same - 1 turn out from all the way in. I will try adjusting that.
[*]If that doesn't work, next step is swapping the parts one at a time to try to isolate the problem - spark plugs, coils, carbs
[*]The carbs were rebuilt by me a long time ago. I may tear into it and look into that after the above.
[*]I haven't tested using a compression tester yet, someone told me that since it's a rebuilt engine, it wouldn't give an accurate reading before it was broken in anyway, true? The thumb-compression test seems to pass though.
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I think that is all, any help would be much appreciated!

Take out the right spark plug and put the plug wire back on it. Hold the end of the plug to the motor to ground it and watch if it sparks. May help rule out ignition.

Don't run with the spark wire open though. It can damage the Pamco unit. Grounded plug scenario is ok as previous poster said.

Can i ask where u got the pamco unit? I searched for one for a longtime before i sold my 350.

Do a resistance test through each side. See if they match.

Sounds like its between the unit and the plug somewhere. Wires, ign coil, cap. Test them all.

Check your battery.

It's very common for the Honda twins to start dropping a cylinder if the battery is low on voltage.

So I swapped the spark plugs and fired it up. Both cylinders fired (!) BUT the right was not...healthy...it would pop and smoke would come out of the exhaust. I messed with the fuel air screw and then it seem to die on me again. I also wanted to check the timing, but with the alternator cover off, all the oil was draining out so I need to go get more oil now....

Sonreir is correct. Start with the simplest cause/solution. A shitty battery will absolutely cause one cylinder to fire poorly.

After you have proven your battery is charged (and good/holding said charge) then Start looking at resistance and conductivity in the wires and coils. You might have a bad wire, or just need a freshly cut end, or you might have a bad resistor cap, or a bad coil.

Also, side note an almost empty fuel tank can also cause one cyl to crap out before the other.