When you press a Pushbutton (X2) it should stay ON. Since my pushbutton is momentary, seems like it will turn ON green light permanently only if the Green light is ON(blinking.
Lilocomotiv, in this case the condition of the Green light will NOT affect the way X2 works. Becasue X2 is a parallel branch, when it is ON, the Green light will be on. Period.
I agree with Bernie. Your X2 is labeled "Control Power Sensor". If this is not true, then you need to correct the label to describe what it actually is, a Pushbutton (if you are correct).
However I do not believe that X2 is a pushbutton, and the difference between a pushbutton and a Control Power Sensor relay (that may be partially controlled by a pushbutton) is large enough to keep you from ever getting the logic to work.
Now, studying your rung carefully, I do see a Pushbutton C1, and it will turn on the green light and latch it on (whether or not the light is blinking) IF the Auto, Caution, and Warning pushbuttons are all off AND the Sentry relay Y0 is on. Did you mean to refer to Pushbutton C1?
PS: What in the heck are Caution and Warning pushbuttons? I have seen Caution and Warning lights but never have I seen those functions carried out by pushbuttons. (This is a new type of retro-control, I suppose, where the burden for safety is put back on the operator!) Are you sure that you should not relabel these to be Lights instead of pushbuttons?
You may think these little errors are just human nature, unimportant, and you don't have time to fool around with them. If you think like that, then you need to change to another field. I tried to think of a career where details do not much matter, but I could not come up with one. Anyone have any suggestions? Maybe a TV news reader, where someone else makes the decisions about what is important and writes the scripts for you to read?
That aside, a momentary button that turns something on the first push and turns if off the next push, is a common problem and has been solved, discussed, and beat in the head in past posts on this forum. Do an "Advanced Search" for keywords alternator, toggle, or flip-flop (although techincally it is not a flip-flop).