We have a cue for each required gait, which actually came with our "big" horse when we purchased him 16 years ago. They made so much sense to us, we continued to use them for the rest of our horses. I can't stand "random clucking" and kissing for "go forward". I want my horses to know how fast to go, too.
For walk, we use one cluck and the word, "walk".
For trot, we use two clucks and the word that corresponds with the "speed" we want, i.e. "trot" for working trot, "jog" for slow trot (not a true western jog), and "trot up" for a strong trot.
Kiss is for canter.
We also use "come" and "get" for right and left which is beneficial for the tandem. (I have found myself giving my husband directions using "come" and "get", "Come at the next stoplight"
) We also use the term "hard" for sharp, tight turns. (BTW, Gee and Haw are draft terms, not really used in the carriage ring, unless you want to sound like a yahoo.)
"Stand" = don't move a muscle.
"Ho" = stop forward movement, but it is different than "stand".
"Back" for rein back, and "step up" for short movements forward (like in line up).
"Over" for sideways movement.
We use "Foot" with a tap on the ankle for pick up your foot (in the stall). It really saves your back from hauling up on their leg. Our horses learned it quite quickly.
"Through there" is "go through that obstacle". It just helps them focus on where I want them to go.
I have a verbal cue for half-halt, too. "Hep" is a "pay atttention, I'm going to tell you something" cue. It is always used in a down transition to give smoothness to the transition. Before we ask for a "ho" (whoa), we "hep" first. We use "hep" before a hard turn, to give them warning. I also use a drawn out "heeeeepp" for "knock it off and listen, stupid" (Yup, our horses aren't perfect!). There are some people that use "and", such as "and walk", "and whoa", but it don't want them to get it confused with "stand".
Myrna