The screw that holds the lever to the switch is too tight. Back it off about 1/2 turn and see if that solves the problem; the switch may be binding and not allowing the internal contacts to move to their correct position in the neutral (no turn) position.
If you try to take the switch apart, you will likely have great difficulty (at best) putting it back together.
If no luck just by unbinding, since the problem has persisted across two different turn signal switches, and you say the wiring was hacked, I think I would take a hard, careful look at all the wires before trying another switch (that said, I'm out of switches, but if it turns out I sent you a bum switch, I'll replace it when I get more).