By the sounds of it the TT600 has a handlebar mounted decompression lever? The TT model must have been a Europe version of the XT or something like that, none of my OEM parts sources lists a TT600. I found a picture of a TT head and it has the same decomp. lever and bracket as mine so the handlebar perch and cable from a TT should be a direct bolt on.

I did rotate the kick start lever by hand slowly till it hit tdc and just barely went passed it, my brother gave it a good kick and on the second try it fired up and ran smooth, no squirting gas down the sparkplug hole first. It idled smooth with no miss or stumble for about a minute then slowly started to do its normal uneven firing.

We went for a 15mile ride and it ran fine with just the stumbling at 2600 to 3200rpm range, above that it didn't miss. Once warmed up, at idle it sounds like it fires only every other compression stroke instead of each one. Doesn't die or seem to even want to die but just has that slow and steady pattern of firing. Motor is dead quite as far as ticks or knocking.
I did notice that my headlight dims each time the turn signal blinks( engine at or just above idle rpm), I think it's normal for that age of electronics. I'm going to switch all bulbs out with LED's if possible.

I'm hoping to get a spare cdi and coil to swap out as a possible cure to the missing(unless this is the normal way these engines run, as I said, this line of bikes is new to me). I doubt it though.
Thanks for all the help and suggestions , it saves lots of hours of guessing and parts changing(when they are not needed).