Bryant force air furnace, Model 394GAW036100, This is an old furnace.

Circulation fan fails to start intermittently (most of the time) when on auto. Fan runs fine in manual mode. Burner comes on but appears to cycle rather shortly. I know that the limit controls the upper limit of the burner. Does it also control the starting of the fan at the lower limit. Another way of putting it. Does the limit switch also act as a HI-LO switch. Will a faulty limit switch cause the fan to fail to start.

You have a defective fan control. On a Bryant many times it is a combo control. A faulty fan control will cause the blower to not operate correctly.