I have seen a wiring diagram for the GH-18 a while back, and that was definitely the single phase motor version, it used 2 contactors for forwards and reverse and a timer for the auto tapping function (it may have also used the timer when you pressed the opposite direction button as well, but i'm not sure)
I think it was a 4 pole contactor for forwards, another other for reverse with the connections to the start capacitor switched…so it gets the 'push' in the other direction at start up to rotate backwards,
And a timer relay between them,
When the microswitch for the bottom of quill stroke is triggered it cuts power to the forward contactor and triggers the timer, when it finishes counting down it then triggers the reverse contactor,
The timer is needed as a single phase motor needs to be fully stopped before reversing it, if it's still rotating even a tiny bit, it will just carry on in the original direction when power is re-applied….this is due to how single phase induction motors work (i'm no expert here, i know just enough to be dangerous… please correct me if i'm wrong, i'm always learning)
On my GH-18 (and a few others i've heard of who mentioned the VFD with as much surprise as me at finding it and a 3 phase motor on the mill… especially with no mention of it from warco) there's just a through connector block on the inside of the back plate of the yellow control box, that's where the contactors and timer were located on the single phase motor versions.
So now to reverse the motor, a signal is sent to the VFD from either the reverse switch or the tapping bottom out micro switch, and it ramps the frequency down to zero which stops the motor (not sure if it applies motor braking as well, but the motor stops fast) it then swaps 2 of the phases to the motor (virtually i guess, as at least 2 of the phases are made by the VFD) then ramps the motor back up to it's original frequency… in t'other direction, this is accomplished in under a second.
So the motor direction switches on the front of the yellow control box are just switching signal wires to the VFD it seems, and the VFD is doing all the magic like motor braking, almost instant reverse, motor start speed ramp up etc.
Of course, being a cheap chinese VFD, it takes a few seconds to 'boot up'…. or more likely charge the capacitors up when first turned on,
And a good thing is the fan on the VFD only runs when the motor is running, sure a temperature controlled fan would be nice, but it's better than the VFD's that just turn the fan on when power is applied to it, there's space for 2 fans in the bottom of the VFD case, i can't imagine the racket of 2 of them buggers howling away, one is enough.
And no, i still havent cut any metal on it (i don't think i'll actually use it, i'll just keep it as an ornament so it's in perfect condition when i sell it on 
I only just got it lifted onto the workbench today (used an engine hoise) and i've just started removing the yellow shipping grease that is slavered all over it, it looks like the measuring tape on the front of the X axis is stained by the stuff, and no amount of acetone is removing it, and i'm worried i'll take the printed markings off the tape soon (and yep, I have removed the film that was covering the tape.. but it did take me a while to notice that)