My S13 has a hose that's leaking rad fluid and is located behind the manifold.

I've looked everywhere and can't seem to find the name of this hose,at first I found rear coolant line/hose but then I found that's for the automatic.

Secondly, I have people insisting the easiest way to replace this hose is to pull the motor *sigh* and say it's one hell of a pain to replace otherwise.

Anyone know wth this hose is and has anyone replaced it and can give me a heads-up on what to expect? Is pulling the motor really my best option?