John- the ignitor does not stay on for the duration of the running time. It only stays on for the first 5 seconds. This is long enough for the flame to ignite and perpetuate itself, assuming the fuel delivery system is up-to-par. The photocell monitors the flame
color and if the flame becomes off-color then the photocell tells the control board to shut the unit down. Naturally, too rich or too lean affects flame color.
Now, I'm confused by your description "the heater cycles 3 times". Tell me more.
I'm glad to see that you checked the pump pressure. Have you used soapy water to check for air leaks all the way to the nozzle? A leak in the airline, fuel line, or a crack in the nozzle adapter will cause no fuel delivery, or reduced fuel delivery as well as reduced atomization of the fuel - all of which can cause a lack of combustion. A restricted fuel filter will cause starvation.
Eliminate all possibilities of a fuel delivery problem before you start blaming electronics because there is not much way to test the board or the photocell successfully without
DESA's diagnostic tool. Unfortunately, replacement of the componants is cheaper than the tool.