If you throttle up on taxi and give no TX rudder input at all, does the plane want to weave from side to side on it's own or merely maintain either right or left tack alone? Answering that question will give you a better idea of what is wrong.

And yes, the tail-wheel should be well aft of the tail-wheel assembly's pivot point or hinge.

Possible problems:

1. Slop in control rod at servo or rudder horn or both.
2. Control rod flexing.
3. Tail-wheel wire diameter too small for tail-wheel hub.
4. Tail-wheel wire slop at rudder attach point.
5. Excessive gap between rudder and vertical stabilizer (fin).
6. Loose hinge, hinges.

check it out......