== Cryptography nargery ahead! Feel free to skip! ==
Herewith, my thoughts about the Kryptos puzzle.
1) The words "BERLIN CLOCK" are useful as hints to the cipher. But the clue about the Berlin clock itself is probably a red herring at the level we've reached.
If that clue hadn't been given, you'd only have found the reference to the clock once you'd solved the cipher where you already needed to know about it.
(On the other hand, it could be a cryptic definition of the Enigma machine.)
2) no part of K4 can possibly require knowledge of the solution to the stage afterwards. (You would think this would be clearer, but people don't always note it.)
3) [this one thanks to Kit] All the messages so far are about burial. Thus:
a) There is possibly something buried in real life, although probably not at the coords given; burying important clues on CIA land would make the puzzle unsolvable by the public, and too easy for the CIA staff who would have seen it built
b) K4 (the passage containing "Berlin clock") is about burial; how can that be?
4) the ideas of burial, and "layer two" etc, make me suspect that Kryptos should actually be read in three dimensions: the "z" axis is some ordering of
0 and 1: the two ciphertext squares
2 and 3: the two Vigenère squares, which may as well be treated as part of the ciphertext for K4 (we might not need to use them)
4 and 5: the plaintext of 0 and 1, not all of which is known
and that each letter of the K4 ciphertext should be read as a coordinate. It's presumably significant that the codeword for K1 was PALIMPSEST, i.e. a document buried beneath another document, and the codeword for K2 was ABSCISSA, which means "x-coordinate".
5) we know from the "BERLIN CLOCK" clue that there are as many characters in the plaintext as in the ciphertext.
6) I am going to assume that if we knew all three coordinates for each position in the ciphertext, then the character at that position is the plaintext.
7) [this is speculative] where could we get a coordinate?
a) it's the same as the row or column of the ciphertext symbol
b) it's constant
c) some row or column of the characters on the Vigenère tables is a label for the axis perpendicular to it— not necessarily always the same one
d) it increases arithmetically and wraps as needed
8) There is a linebreak between "BER" and "LINCLOCK", which may be a hint that position is worth paying attention to.
9) the columns are 16 characters tall. The text of K4 begins at the 64th character on its panel, counting left to right and then top to bottom. 64 is a simple multiple of 16.
9) I have done some analysis, but not enough.
You can test a hypothesis by matching the letters BERLIN to NYPVTT (forwards), or vice versa (backwards).
I have written a Python script to check some of these, though it only does horizontal lookup: https://gist.github.com/marnanel/90f256b17b8cd4a98724ede9a95ca6b8
I must apologise for the lack of description here: I wrote the code and made the images in 2019, and only just found it again-- so I don't have the full details.
The x and y of each chart are the rows of each panel of ciphertext. If there is any instance of any of the desired mapping pairs from the "x" row to the "y" row, the square at that junction is striped in the colours for that pair; otherwise it's grey.
If there was a full match, you would see a row or column of [red, orange, yellow, green, blue]. There is no such line, but "forwards" has a match for the first four, and "backwards" for the first three. And, as I said in point 8 above, there is a linebreak in the original after BER. So either of the two examples of strips of rainbow squares matching BER might turn out to be half of a positive result.
Further exploration is needed!