A naive suggestion?

Do people who feel suicidal usually try to hide it when asked directly?  Googling around indicates it is generally thought that they don't.  For example, from the book Psych Notes: Clinical Pocket Guide, we get this:

Would it hurt to have this question on the pre-flight check list that all pilots ask each other? 

What they do now seems not to be direct enough:

The FAA expects pilots and airlines to take joint responsibility when considering if a pilot is fit for duty, including fatigue resulting from pre-duty activities such as commuting. At the beginning of each flight segment, a pilot is required to affirmatively state his or her fitness for duty. If a pilot reports he or she is fatigued and unfit for duty, the airline must remove that pilot from duty immediately.

Update:  I heard some aviation expert or other on the TV saying that if the co-pilot really wanted to kill himself and passengers, he could almost certainly circumvent any procedural changes.   And I have heard Senator Leyonhjelm say, in relation to gun suicides, that people determined to suicide will find another way in any case. 

Apart from Leyonhjelm simply being statically wrong, this line of defeatism seems to me to pay no attention to the psychology of suicide.  If you can make impulsive acts harder to finish, you do reduce suicide.