"Bill Denton" wrote in message
...
As separation is a function of traffic control, when would traffic control
not include separation?

Separation is not always a function of traffic control. In fact the AIM
says for Class D airports "No separation is provided for VFR aircraft." The
AIM is very clear as to what traffic services are provided for each class of
airport.

Who would be responsible for separation and sequencing under these
circumstances?

Ahhhh that would be you Bill, by the use of your eyes. The guy in the tower
with binoculars just doesn't cut it for separation or sequencing and the FAA
realizes that.