Both are hot with the key on. (lights or no lights) Not really sure what the blue wire was intended for being that it does'nt show up on the wiring diagram.
As far as the white wire in the engine compartment:
The
BX1800 has the D722 engine with the fuel stop solenoid that momentarily pulls the fuel linkage to the off position to shutdown the tractor, mounted just below and behind the air filter. The
BX2200 has the D905 engine which has a solenoid that continuously holds the fuel on and is powered as long as the engine is running, mounted to the rear of the injection pump. The wire harness for both models is the same but the two engine shutdown systems are wired different. The
BX1800 requires only the white lead near the air filter for the system to operate. On the
BX2200 it requires a 3 wire connecter to the solenoid and the white lead to the "motor side" of the starter. The continuous solenoid, being smaller needs more help to initially engage the fuel rack, once the start position is released and the solenoid has engaged, it is held in position by the red/black wire in the 3 wire connector.
So the
BX1800 has a 3 wire connector (white from starter, red/black continuous power, black ground) located near the front of the air filter and a single white wire dangling around the starter area. The
BX2200 has the single white wire hanging around the air filter not doing anything.