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I've had this issue for a couple of months now and I only just now saw this... Is it a heater core leak? Always leaves a nice trail and magically, all of the coolant in the reserve is gone.
This "mystery" tube on the passenger side, by the exhaust. Note the "dark spot"/dripping fluid.
Fully-illuminated area
I can see what looks to be the 2JZ-GE's Heater Control Valve lower hose in the upper part of the last photograph. The "Mystery" hose that you are speaking of is actually a condensation drain line for the air conditioning system. It is normal for that line to leak some moisture onto the ground whenever the A/C has been running, especially when it is hot out. All vehicles with air conditioning systems have some form of condensation drain line like this.
A heater core leak in these cars seems to be either from the engine bay side where the brass fittings come through the firewall or from the inside of the vehicle somewhere along the heater core unit itself.
As Kahn says, water from that hose is condensation on the evaporator core. The heater core is not in the same place, you would see it in the floor board or outside but closer to the center of the car. The heater core is directly behind where the heater hoses connect at the fire wall. If you are losing significant coolant and it's not in the floor board and not leaking under the car, you may have more serious internal engine issues.
As Kahn says, water from that hose is condensation on the evaporator core. The heater core is not in the same place, you would see it in the floor board or outside but closer to the center of the car. The heater core is directly behind where the heater hoses connect at the fire wall. If you are losing significant coolant and it's not in the floor board and not leaking under the car, you may have more serious internal engine issues.
^^ What RXRodger said. If coolant loss isn't coming from a leaking heater core, a bad hose somewhere, a radiator leak or a loose screw on the exhaust side of the block that blocks a coolant passage hole by design... then it might be a good idea to get a twin tube fluid head gasket testing kit from Amazon and to send an oil sample off to Blackstone to see if there is any indication that there's an internal coolant leak between the gasket and the head.
That might not be the issue but it's good to check if there is no other indication of an old hose that is leaking or if you can't find any component that has coolant flowing through it which has developed a leak.