Gold Digger, The 268 flasher has only two terminals- "X" and "L". The X is fused power to the device. The L is load, what you get when the Signal-stat lever connects the right or left lamps. The Signal-stat indicator lamp (there is only one, it moves under the green and red windows with the lever) is normally powered by the "P" terminal (pilot lamp) on a three terminal flasher. Likely someone jumped the L to the P somewhere to make the indicator pilot light work with the two prong flasher.
What is happening: The 268 'sees' the indicator lamp as a load but it is not sufficient to trigger the thermal interrupter within. Thus the center red light shows. When you move the lever the actual turn bulbs are added to the load and it flashes normally.
Even if you have a good 3 prong X-L-P flasher it will not work properly if the jumped L-P connection is not removed. AFTER this correction is made the 268 will not flash the indicator at all, red or green. The indicator can then be made to work properly with the two-prong flasher by adding two 1N400x diodes. One from the left Signal-stat output, one from the right, to the "P" terminal wire.
The 535 is not the only use-able 3-prong flasher. As a matter of fact, it is a poor choice because it is not specifically load dependent and will not tell you if you have a bulb shorted or open. OEM's never used that type of universal flasher. They were sold by parts houses as a 'universal' replacement for many load specific part numbers. What they conveniently never mention is that the 'universal' or 'heavy duty' flashers rob you of the ability to monitor burned out or shorted lamps. The flasher just keeps clicking away at a relatively constant rate even if one lamp is out or shorted. 6V cars with one front, one rear turn bulb often used #181 flashers. These are still plentiful NOS.