The oldest manuscript we have of John is in the Codex Sinaiticus. In both verses, it says, “life eternal.” It’s in Koine Greek, on papyrus, dated 350 AD. I photographed the two passages from the Codex Sinaiticus. John 4:36 is here: (pdf) John 6:40 is here: (pdf)
Scroll down to see the actual, handwritten manuscript.
For John 4:36, go to the second column to the left and scroll down to the 6th line -there, you will find “life.”
“Life” looks like: ZWHN
On the 7th column below it, you will find “eternal.” It looks like: AIWNION
For John 6:40, go to the third column to the left and scroll down to the 11th line. Both words are on that line. They take up the whole line.
“Life eternal” looks like: ZWHNAIWNION
There is a dot after "life eternal" in John 6:40 (on the manuscript) and if anyone knows what it means, I’d like to know. Jot or tittle? It doesn’t appear in John 4:36.
You realize you’re looking for life eternal? I already found it! :o)
Why did the translators transpose the words in John 6:40?
I don't think the answer is convoluted; I think it's simple. The entire bible is transposed, why wouldn’t they transpose here? They stayed true to the text in John 4:36 (life eternal) because it’s understandable when translated correctly; the reference is to fruit and it even sounds poetic. Incidentally, this verse (in English) is actually (partially) metered (syllables stressed and unstressed); changing it to “eternal life” would destroy the meter. In John 6:40, I think they transposed the words because the reference is to man and it sounds weird saying: “everyone who looks to the Son and believes in him shall have life eternal.” Reading John 6:40 as “eternal life” does not affect the meaning of the verse.