
The Bay Area murderer gave us three ways to identify himself as the author, by using "Zodiac" and his "crosshairs" in numerous communications, and "Me" (only once) in his Exorcist letter on January 29th 1974. The question being, why did he use "Me" in 1974 when he could have just written "Zodiac" or added his "crosshairs"? The Zodiac Killer usually had purpose beneath his assumed madness.
The answer probably lay in the verse he added after writing "Signed, Yours Truley" in the Exorcist letter, which carried the 8-letter phrase "My name is" in the extended version of the "Tit-Willow" verse. Only one communication carried all three signatures of the Bay Area murderer if you apply the following logic.

He gave us the answer to his Z32 code by writing "P.S. The Mt. Diablo code concerns Radians + # inches along the radians" one month later, on July 26th 1970. Both "radians" and "inches" could be found in the Z32 solution, so why not "Me" in the Z13 solution. The Zodiac Killer, in mocking fashion, may have been giving us the answer to the Z13 code in the most simplistic of terms. A signature he would corroborate on January 29th 1974 when he unusually added "Me" to his letter. This is the only Z13 solution ever presented as a "signature" that was replicated in a later Zodiac Killer communication. The April 20th 1970 and January 29th 1974 letters would now carry both "My name is" and "Me" in each instance.

If we know that replacing ciphertext characters with plaintext characters can never produce a verifiable answer without later validation, then the Zodiac Killer almost certainly knew it.
The technique of rotating an outer circle of characters around an inner circle of fixed characters by a desired number of positions was ably covered by Edgar Allan Poe in "A Few Words on Secret Writing".. He wrote about this immediately after detailing another technique of splitting the alphabet into two lots of 13 characters, A through M, and N through Z. Odd therefore, that the Zodiac Killer would create a code of 13 characters beginning with A and ending with M, which when rotated by 8 positions on a circle, would create a signature later used in the Exorcist letter. Both of these techniques coming after Edgar Allan Poe described the scytale method of decryption, that can be used to solve the Zodiac Killer's 340 cipher. A cipher that Zodiac referred to when opening his April 20th 1970 letter, stating "By the way have you cracked the last cipher I sent you?".
We have two techniques described in "A Few Words on Secret Writing" that when combined and rotated through eight positions, gives us a signature used in the Exorcist letter. However, it may just be one of those massive coincidences.
FURTHER READING: DEATH IN PARADISE