HELP with EOG based Morse Decoder

an A would be represented by two dashes

That would be M. A would be dot-dash.

You will need to describe the electronics and its outputs much more clearly. This does not make sense:

a positive peak(max) represents left eye movement and the minimum peak represents right eye movement.

The Arduino ADC can read only positive voltages, 0-5V on a standard Uno.

Obviously, timing is very important. Use the millis() function to keep track.