IMO an Action Points system isn't quite the right thing for Gearhead, but the idea definitely merits some serious consideration. I'd love to see movement and actions be handled separately (or just handled better in some other way). It's just kinda hard to figure out a system that accomodates that and is still not a pain in the ass for things like walking around in a city or dungeon 
There are a few examples of games that use Action Points we could look at. Front Mission and MissionForce Cyberstorm come to mind.
On one level, it's pretty simple to deal with this; you just have one clock for the PC's reaction time and another for the mech's motion. Each time the PC's reactions are ready, they can shoot or change speeds or directions or whatever. The mech motion proceeds independently, moving from square to square at whatever speed the mech is able to manage. You need multiple clocks anyway for multiple weapons waiting to be ready.
My idea was to have one clock for movement actions and another for combat actions. Movement actions could occur either at every n ticks, or at every square regardless of how little or much time it takes to reach the next square. Combat actions could occur whenever a weapon cools down and becomes available with maybe a short mandatory resting period between each shot.
That said, if anybody was willing to make the change to a 100% action-point tactics game, I'm all in. The big differences would be as follows: There'd be a distinction between "combat mode" and "travel mode", at least as far as the UI is concerned. No more facing, which means that "paper doll" style characters + mecha would finally be possible. Weapon ranges would be greatly reduced; a single map could hold multiple combat encounters, leading to more complex missions/scenarios. I see it as something like "Super Robot Wars" meets "Dungeon Monkey Unlimited".
I'm not sure what you mean. Why would there be no facing? And why should the combat and travel modes be distinguished? I know there are games that limit you to one movement action followed by one combat action, but there are others that allow you to perform any action as long as you have sufficient points, and make facing important.