Most of the shifter cables I have seen are only 3/16" (#10 threaded end), but the outside of the sheath may be 5/16 or 3/8". Many shifters are harder to move then the electrical main cut off switch.
The rule is the rule, I can't change that. IMO, a 3/16" rod 12" long is not stiff enough, but a 3/16" morse cable with thick outer sheath is strong enough (if I was making the rule).
A 30 series Morse cable has #10-32 ends
A 40 series Morse cable has 1/4" ends.

I like the comment about it being a secondary mechanism.