Oil leak at rear of engine seems to run down between transmission and engine only when it is running

manual transmission hold grease rather than fluids. fluids that run around that area would be fuel, and break fluid to the rear.

Your radiator needs to be replaced. Chances are you have transmission and oil cooler lines going through them and there are mixing inside the radiator.

Try running some of that high-mileage engine oil next time you do an oil change (it helps to swell engine seals slightly). If the problem clears up or is reduced, then it's likely that the rear main oil seal is starting to leak a little. The rubber seals will harden up and shrink a little with age.
I would also powerwash the entire area clean, so that way any leak will be easier to monitor and pinpoint.

Look at the top of the engine /trans connection area for a leaking seal.Clean that area then check there.

Oil leak can be attributed to several factors.
1. Gasket failure.
2. Uncontrolled Crank case pressure Failure.

RECOMENDATION:
Tighten both the valve cover and oil pan bolts.
Replace the Positive Crankcase Ventilation Valve and vacuum line.,

INFO: PCV
This is a valve causes a negative vacuum on the engine while its running, As to say if it had a leak in a valve cover it should not be leaking while its running, only when the engine it turned off.

Hope this tip guides you in the correct direction to solve this problem.

R/
David

Overfilled is not good but it would have to be very high to cause leak,There are numerous places in rear of engine that could be leaking.could be leaking from rear of intake,the oilpump drive o ring,but most likly leaking from rear main seal that seals at the rear of the crankshaft and the transmission will need to come out to access this seal. you will need to have the oil leak diagnosed to locate the exact spot.

Could be the oil pan gasket or the rear main oil seal.
Remove the torque convertor cover. ( I am assuming that your truck is an automatic) That's that thin metal cover between the engine and transmission on the bottom side.
Drive the truck around the block to warm up and the oil to start leaking.
With the engine running in neutral, emergency brake on and wheels choked for safety.
Crawl under the truck and see where exactly the leak is. Is it between the flywheel and the engine block --leaking straight down the center of the flywheel --crankshaft rear seal?Or the pan gasket? or even a oil galley plug?
Good Luck.

This is most likely a leak from your rear main seal. It happens and can be a pain to replace if you're a DYI kinda person without the nec. equipment.

1. Raise and safely support the vehicle with jackstands.
   
2. Remove the transmission.
   
3. If equipped with a manual transmission, remove the clutch and pressure plate.
   
4. Remove the flywheel assembly.
   
5. Using a suitable prytool, carefully pry the old seal out.
   

6. Inspect the crankshaft for nicks or burrs, correct as required.
Crankshaft rear main seal - 5.7L engine

To install:

1. Clean the area and coat the seal with engine oil. Install the seal onto tool J-34686 for 3.4L engines, J 41349 for 3.8L engines or J 35621 for 5.7L engines.
   
2. Install the tool (with the seal mounted to it) onto the rear of the crankshaft. Tighten the screws snugly to be sure the seal will be installed squarely over the crankshaft.
   

Exploded view of the rear main seal installation - 3.4L engine
Click to Enlarge

1. Tighten the wing nut on the installation tool until it bottoms out.
   
2. Remove the tool from the crankshaft or rear oil seal housing, as applicable.
   

Rear main seal and installation tool - 3.8L engine
Click to Enlarge After position the seal on the tool, install it to the crankshaft housing

1. Install the flywheel.
   
2. If equipped with a manual transmission, install the clutch and pressure plate.
   
3. Install the transmission.
   
4. Check the fluid levels, start the engine and check for leaks.
   

The problem is ,Your rear main seal is bad

would suspect that it is a rear main oil seal in the engine...not good and costly to repair since the engine and transmission need to be seperated for a 10 dollar part. is it oil that is leaking?