Coolant is leaking. Was told it was the water pump, but a mechanic said that it was one of the smaller hose in the back beyond the engine. What is he talking about?

Sometimes it can be difficult to determine the location of a leak when it is severe. The first thing to do is clean the affected area. For engine coolant, this can be done using water from a pitcher or garden hose. Next, slowly add more coolant to the radiator (only when the engine is cold) while watching for the leak to present. Note the general location of the leak whether it's the engine area or radiator area. Coolant leaks from the engine can originate from the water pump, gaskets or hoses. Coolant leaks from the radiator can come from the radiator or hoses. There are also coolant hoses that run to the bulkhead/firewall and coolant reservoir that could be leaking. In my experience the most common major coolant leak comes from a faulty water pump. When a water pump leaks it tends to get coolant on the serpentine belt which then slings everywhere! You can read more here: https://www.yourmechanic.com/article/symptoms-of-a-bad-or-failing-water-pump

Could be welsh plugs on side of engine are corroded.
Could be a smaller pipe like a heater hose pipe or an auxilary cooling pipe .Had one of these little extra pipes on a mitsubishi sigma under the inlet manifold that was leaking.
Did you use a coolant in the engine as water can corrode welsh plugs in engines as I found out on my car !.

Yes, you are running hot from leaking all your coolant out. No one can tell you where it is leaking without looking at it. Could be a hose leaking, the radiator, a bad head gasket or intake gasket, the water pump...if coolant is leaking from the front of the engine, that could be the water pump or radiator hose or a water pump gasket. Pretty common for the water pump to leak when it is worn out, that's how you know when to change it.

When you fill the radiator and overflow tank back up to full, does the engine still run hot? If it does, I would not advise running it-have a shop diagnose it before more serious damage occurs. Head gasket repairs can get very expensive-that is the danger you are facing, and if the head gasket has already gone bad from overheating, continued running of the engine can cause you to have to replace the engine. Overheating is a major cause of early engine failure.

Try to determine where the leak is, from where it drips off the engine. The coolant constantly circulates from the engine to the radiator and back into the engine. The heater hoses circulate coolant from the engine to the heater core in the heater case and back into the engine. Besides the overflow tank, these are the only places coolant would be on the car. The engine can leak coolant from a lot of places, but if leaking to the outside, you should be able to spot where it is coming from. Good luck.

when the head gaskets were done did they check for cracks in the heads?

see this causes and fix it. God bless you
Water pump -- A bad shaft seal will allow coolant to dribble out of the vent hole just under the water pump pulley shaft. If the water pump is a two-piece unit with a backing plate, the gasket between the housing and back cover may be leaking. The gasket or o-ring that seals the pump to the engine front cover on cover-mounted water pumps can also leak coolant. Look for stains, discoloration or liquid coolant on the outside of the water pump or engine.
Radiator -- Radiators can develop leaks around upper or loser hose connections as a result of vibration. The seams where the core is mated to the end tanks is another place where leaks frequently develop, especially on aluminum radiators with plastic end tanks. On copper/brass radiators, leaks typically occur where the cooling tubes in the core are connected or soldered to the core headers. The core itself is also vulnerable to stone damage. Internal corrosion caused by old coolant that has never been changed can also eat through the metal in the radiator, causing it to leak.
Most cooling systems today are designed to operate at 8 to 14 psi. If the radiator can't hold pressure, your engine will overheat and lose coolant.
Hoses -- Cracks, pinholes or splits in a radiator hose or heater hose will leak coolant. A hose leak will usually send a stream of hot coolant spraying out of the hose. A corroded hose connection or a loose or damaged hose clamp may also allow coolant to leak from the end of a hose. Sometimes the leak may only occur once the hose gets hot and the pinhole or crack opens up.

IF LOW COOLANT LIGHT CAME ON ENGINE SHUT OFF BECAUSE IT GOT TOO HOT AND OVER HEATED.WHEN YOU HAVE LOW COOLANT.YOU COULD HAVE LEAKING RADIATOR.YOU COULD HAVE LEAKING RADIATOR HOSES AND WATER PUMP. ADD MORE COOLANT IN CAR RADIATOR UNTIL YOU AT FULL COLD MARK ON THE OVER FLOW COOLANT TANK START THE CAR LET IDLE UNTIL ENGINE GET OPERATING TEMPERATURE.RAISE YOUR HOOD LOOK FOR LEAKS THE RADIATOR PRESSURE WILL PUSH COOLANT OUT WHERE LEAKS COULD BE.LOOK AROUND RADIATOR AND COOLANT HOSES.LOOK AT WATER PUMP.IF YOU SEE COOLANT LEAKING AT WATER PUMP REPLACE IT.

There are a few connections ports that need to be checked. if you cannot find the leak at these places then that happens at the seal of the water pump. When the water pump seal is bad then time to replace the water pump. Why? it is the same labor for the job. Hope that you don't get overheat. This is happening when your water pump is not turning: broken bearings.

Therefore check these following connections first, sometimes the rubber hoses get deteriorated then the clamps need to be tightened to minimize the leak.
1- Upper hose connect to radiator.
2- Lower hose connect to bottom radiator and engine port that is water pump inlets
3- Over flow hose.
4- 2 Heater hoses coming to the fire walls.
Hope this can help.

check the water pump weep hole on the bottom of the pump or the freeze plugs in the block,heater hoses going into the firewall,.

yes it has freeze plugs,water pump may be leaking,fuel pump has nothing to do with coolant leaking

Some of this below I wrote to another person and copy/pasted it here so it directs to the water pump incase that's your issue. If your leak is on the driver's side of the engine read the last paragraph, if not... maybe you have a ruptured radiator hose that connects to the block below your distributor. Another hose is the obvious one in front that goes from the top of the radiator to the head. In the back of the engine there's a hose that runs coolant to your heater core and another hose that returns the coolant back to your motor. Those are smaller hoses than the 2 main ones.

Do you need a new water pump, the bearing might have went out in it and it has a "weep hole" that lets the coolant near the driver's side front tire (on the engine block) out to let you know what happened, rattling is a good indicator too. Change the timing belt at the same time and you'll be good for the next 125k miles. Don't drive it any more or you will possibly warp the head or ruin the head gasket. The cost is about $350. for all around here in central Ohio, don't know where you are but hopefully it's not more than that. If you try to do this yourself you will also want to learn how to set the timing. Good luck.