[Steeveedee]

I don't know what the "T" terminal is. The starter solenoid has the main battery cable connection, and the "S" for start and "R" for reduced voltage terminals. "S" is obvious, and the "R" terminal connects via a yellow wire to the coil during cranking only. If you don't have another power source for the coil after you release the jump start button, that would explain it. Also, if you just rebuilt it, you need to get the cam broken in properly. All these false starts can potentially lead to early cam failure.

ETA- you need to have a resistance inline when in the run mode, or you will destroy the points, and possibly the coil. The factory harness provides that. Maybe you should wait until you have the harness installed.