My guess, unless he was ambidextrous, is that he was right handed, going on his writing skills. When writing a T bar, a right handed person invariably strokes the T from left to right, a left handed person strokes from right to left. One almost certain correspondence from the Zodiac Killer was the Presidio Letter on October 13th 1969. You will notice the separate paragraphs on this letter. Subconsciously a person will rest or pause momentarily during paragraphs, before continuing on with the letter, particularly if he is recalling events. At the start of each paragraph when the ink from the pen has fully replenished, especially with a marker pen, it can produce a blotch of ink where the pen is initially laid onto the paper. His T of 'This is the Zodiac Speaking', his T of 'The SF police' and the S of 'School children make nice targets' all show this blotch. Aside from the S, the two T's exhibit right handed characteristics. A left handed person would usually rest the pen on the right side of the T and move right to left and would be highly unlikely to leave a blotch on the left side, as the hand immediately lifts off the paper. Of course this blotch would vary from pen to pen, depending on its manufacture, tip size, ink reservoir, but with some this result will be found. Three paragraphs, three blotches. Therefore it is more likely that if he wrote his letters right handed, he used his weapon right handed, and I stress more likely, not certainly. I am sure that either Michael Mageau and Bryan Hartnell would have indicated which hand the killer used, or at least Bryan Hartnell, after all the killer showed him the gun was loaded, as well as the tying up of the pair and the stabbing itself. It also may be significant that all five entry wounds on Betty Lou Jensen's back were on the right side, in particular at close range, it depends if right handed people err to right!
Traits having significance indicating a person is a left-handed writer:Crossing of the lower case t from right to left.
Leftward drag of elongated i-dots.
Long initial stroke of letters at the beginning of a word which may proceed either in an upward or downward direction.
Hooks and curves at the beginning of some small and capital letters which commence in a leftward direction.
Prominent eyelets in beginning part of the small a, d and g, representing an initial underhand motion.
Overhand motion in forming lower case v (made with retrace or eyelet at bottom) and the lower case h (eyelet formed where loop and hump are joined).
Tenting of lower case h, l, and t; and tenting of the upper part of capital i and j.
Open lower part of the final lower case g and y with the ending stroke curving to the left; also triangular or v-shaped lower parts of those letters.
Absence of terminal endings of such letters as lower case d, l, and t, as well as lower case h, m, and n, with slight pen drags to the left.
The terminal of the lower case s with an absence of a retraced bottom coupled with a leftward extension of the closing part.
Similar to the lower case s, the lower case f and k, as well as capital G, also are found to have considerable leftward extension in their closings.
http://www.jjhandwriting.com/left-hand-and-opposite-hand-writing-features-useful-as-a-basis-of-forming-expert-opinions-of-authorship/