Please Help! Need to know what this hose is/was?

[Blue_Runner]

I know that somebody is going to be able to help me with this. There is this "T" connection in the tell tell line coming out of the port side cylinder if standing behind the boat. It looks like the line coming off the south facing part of the "T" had a hose coming from it that was cut before I got the motor. I can't find anywhere that this hose might have gone. It has a slow drip coming out of it while the motor is running. Your wisdom is apreciated! I've wondered if this might have to do with a water temp guage, but that's just a WAG. What should I do with it?
Thanks,
Blue
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