The proverb
He that will not when he may, when he will he shall have nay
basically states that one should not be too demanding when it comes to choosing.
According to Wikipedia:
as the ancient proverb proposes
it describes it as ancient but there's nothing I can find that links this proverb to a source of some sort. The footnote only redirects me to this broken link.
You can see the contents of the link if you visit the Internet Archive, which actually is just a repost of material from the Oxford Dictionary of Proverbs. It's a list of sources, the earliest of which are:
Nu sceal ælc man efsten, thæt he to gode gecerre tha hwile the he muge, thelæste, gyf he nu nelle tha hwile the he muge, eft thone he wyle, he ne mæig [Now shall each man hasten to turn to God while he may, lest if he will not now while he may, later when he will, he may not].
[a 1000 in Anglia (1889) XI. 388]He that wyl nat when he may, He shal nat, when he wyl.
[1303 R. Brunne Handlyng Synne (EETS) l. 4795]He that will not when he may, When he will he shall have nay [denial].
[c 1450 in Brown & Robbins Index of Middle English Verse (1943) 186]
As it dates back to Old English, it is fair to say it is an ancient proverb.
The actual meaning seems to be "If you cooperate with me when I need your help, I will cooperate with you when you need my help"
"Ancient proverbs" often originate from the Bible, and He that will not when he may, when he will he shall have nay does not seem to be an exception: it repeats the message of the Book of Jeremiah (written c. 525 - 500 BC) in which, the prophet Jeremiah repeatedly tells the people to worship "the one true god" because He is the only god that can help them, and if they do not listen to God, He will not help or listen to them:
From the New International Version
Jeremiah 11: They have returned to the sins of their ancestors, who refused to listen to my words. [...] 'I will bring on them a disaster they cannot escape. Although they cry out to me,* I will not listen to them.
This message is repeated in the Book of Proverbs (written c. 325BC) Chapter 1:
24: But since you refuse to listen when I call and no one pays attention when I stretch out my hand, [...] 28 Then they will call to me but I will not answer; they will look for me but will not find me, ...
Winston Churchill quotes it in Volume 1 of The History of the Second World War. The context is his contempt for 'waging war by committee'. Unable to do as he wanted when he wanted, he had lost his opportunity when permission was granted.
