The design of the FMEL, a floor-mirrored Einstein-Langevin "light clock", is introduced. The clock provides a physically intuitive manner to calculate and visualize the time dilation effects for a spatially extended set of observers (an accelerated "frame") undergoing unidirectional acceleration or observers on a rotating cylinder of constant radius. In both cases, the rate of the clock agrees with the "clock hypothesis" and approximates an "ideal" clock. Inertial and accelerated observers will agree on the length of standard metre sticks that are parallel to the primary mirrors of the clock and they will agree on the simultaneity of events that occur along that line. It is found that the path of the light in this clock is "not" a least-time path between the mirrors, but it "is" the least-time path for the motion of objects restricted to the accelerated frame. It is possible to send signals between observers in the accelerated frame at speeds greater than the speed of light in their frame, but this does not imply a violation of causality. (Contains 7 figures.)