The motor's correct for a Mk3 with single speed wipers. You can use a 2 speed motor, with the 3 wires, if you need a replacement.
As above, there's an ignition live feed to the motor to power it between you turning the wipers off and them parking themselves.
Just ignore the blue/green 2 speed bit.
When you turn them off current flows up the B/LG from the 12v ignition live at the motor connector block, then back to the motor windings via the R/LG (that's also used when the wipers are on & supplied by the 12v at the driver's switch). When the wipers get to the park position the park switch cuts the supply at the motor and earths B/LG - both sides of the motor winding are now earthed and it stops dead. If the park switch didn't earth the motor could run on enough to reconnect the park switch to 12v and set the the wipers off on another lap....
So, if your wipers stop dead as soon as you flick the switch either there isn't a supply to the park switch or there's a break somewhere between it and R/LG terminal on the driver's switch. With the wipers off, continuity between the B/LG and R/LG connectors at the motor strongly suggests it's the park switch. It's not unusual for the little plastic plunger to wear down to the point where the contacts arc instead of earthing and burn out.