I'm concerned there is not equal amounts of fuel coming out both accelerator pump discharge nozzles when you work the throttle. Suggests passages may not be cleaned properly. Question is what else is not cleaned properly.
Idle circuit uses the two idle mixture screws located at front of throttle plate assy.
Gently turn the screws in clockwise until the gently bottom out, then back out about 2 full turns. You will have to adjust them from there. Could write a short book about just setting the idle mix, but you want the fastest idle speed by turning the mix screws while keeping the throttle shaft idle speed at a slow throttle nearly closed setting.
When I rebuild carbs, would be great if you can soak the metal parts in carb cleaning solution. I don't have access to it anymore, so out comes cans of gumout. I do not use any other brand. I'm sure there are other good ones, but some other brands don't clean well enough so I stick to gumout. Buy several big cans, I go thru a couple for one carb rebuild.
I spray off the outside of each part, spray down along the throttle shafts while working them back and forth. I spray clean every square millimeter. I mean it. I spray every hole, if they are dead end holes you'll get a good shot of carb cleaner in your face so wear eye protection. So I spray every hole, the spray will exit a passage way someplace else, so then go the the other end of the passege and spray back the other direction so each passage is sprayed two directions. Do this several times each passageway. Spray out thru each accel pump nozzle. The same amount of spray should come out both nozzles. I have found itty bitty pieces of gravel in some nozzles, had to use a cutting torch tip cleaner or tiny drill bit to remove the grit.
With everything clean I blow every passage out with compressed air. Use more carb spray again if necessary and repeat blow with air again too.
There are idle air bleeds, emulsion tubes, etc that must be spotless. You should be able to eat of this thing when your done.
If the problem is only idle mixture, then the engine should run steady with throttles open part way. If it still won't run, then you have more problems.
I hope this is not a fresh rebuild as you need the engine to start and run steady for 15-20 minutes to properly break in a flat tappet cam.
Sorry to just touch the surface, there's lots of details to be stepped thru solving carb problems.
The TQ is a great street carb, and can be made a good race carb too. I had one on my 340 duster for 140,000 miles. Worked great even worn out. I would put in the brass floats, throw away those foam ones.