that's exactly what I was trying to describe... but a little different
if you look at the direction of the arrows in the second picture you posted, it clearly shows it coming from the rear iron, goes to the throttle body, does it things in there. Then exits the throttle body by the 90 degree soft hose, going into the hard line, then through the hard line to the soft line that is leaking on his right now, then into the water pump housing...
not trying to step on any toes but...
if it does go the way you describe it, why would they use colder coolant for the AWS when a source of warmer coolant is right below it... it also makes more sense to pull hot coolant from the rear of the iron (potentially the hottest coolant in the car) and then send it through the Accelerated warm up system.. not from the cooler coolant coming from the water pump...
it would also be a PITA to try and get the pump to push coolant through that whole rather then use the dynamics of heating and cooling properties and fight the natural tendency for the hot coolant to rise...
To the OP
head here
http://www.rotarycarclub.com/rotary_...read.php?t=563
down load the factory parts index...
open it up, go to the page 40 look on the left hand side, it shows the hose
according to that, the part number is 13-692B
J.