I have 3 of the TT .42GPs and they are normally trouble free.

First, check the pressure nipple in the muffler. If it is closed off, the engine will run for a while until the vacuum builds up in the tank, then it'll quit. If the nipple is clogged up, use a small drill or a wire to clean out the hole.

The TT .42GP has an air bleed carb. As a starting point, the air bleed screw should be half way across the hole on the front side of the carb.

Next, make sure you aren't running too lean. I'd start over by closing the needle, then opening is 2-3 turns. Crank up and leave the glow ignitor on the plug. Lean the engine until it breaks into a 2-cycle. Don't peak it out until you are sure it will stay running.