Help! I need to ID my shifter

That is a strange one. The mechanism looks a little like the Hurst Competition Plus. It is not. The handle would have two bolts going through it to mount to the shifter mechanism.

HOWEVER, the 1966 Dart did not use the Hurst shifter. It used a handle mechanism made by Inland Mfg. Co. It is characterized by a T-handle reverse lockout. Neither the press nor owners liked it, as conversion to Hurst units was common. Chrysler relented during the 68 model year and brought the Hurst linkage back.

Hope this info helps. IMO completing your shifter as a Hurst Competition Plus would be the way to go.