This is a recent problem and one that I noticed today for the first time driving it after about a week and a half, when it was just sitting in parking lot for that amount of time.

Upon startup of the truck, gas just begins to leak at kind of an alarming rate. It's not just a pitter-patter here and there, it's a bit of steady leak. But it seems after it's moving for awhile it stops leaking and I confirmed this by driving in a circle around the parking lot and then re-tracing where I drove by walking and I could see that from where it was parked, it left a trail from where I pulled out but the farther away I got from where it was parked, the trail disappeared.

When I shutoff the engine, the leak stops completely almost immediately.

I was able to snap a picture of the sight of the leak when the engine was running (probably not a smart idea but oh well..) Any ideas?

 

I'm not sure which of those Lines are for Fuel, but neither look in very good shape (rusted/corroded).

I'd cut out the section in question and splice in a new piece.
You also could use Flex if you wanted to.

PS:
I think you should quit driving it until you got this fixed.

 

the fuel line is the biggest line (the one on top in the picture).

How much do you reckon it cost to cut out that piece of the line and replace it? I'm at a severe lack of tools because of where I currently am (military), so more than likely have to take it to a shop.

 

All you need is a mini tubing cutter and a screwdriver if you replace it with rubber fuel line. Military bases have motor pools with mechanics and tools. Maybe you can get one of them to do it for you.

 

oldchevy is right on both counts

At least, check the length of Metal Tubing which is badly corroded,

measure the outside diameter of the Metal Tubing,
buy a (just a little longer) piece of Flexible Fuel Tubing than the bad area of the appropriate inside diameter to fit over the Metal Tubing (needs to be snug),
get four Small Hose Clamps,
cut the bad part out with a Tubing Cutter (2 cuts),
clean/sandpaper the ends of the remaining Metal Tubing,
slip the Clamps on the Flex Tubing,
slide about three inches of the Flex onto the ends of the Metal Tube,
(so that's the length of the cut out piece plus 4-6" of Flex)
separate the Hose Clamps by an inch or so and tighten.
Turn on Ign, and let it fill up... done !

IF you think that more of the Metal Line is bad, then buy enough Flex Tubing to make the distance as necessary.
I have had to replace the WHOLE line (about 15') on a couple vehicles with Flex.

You might have to buy the Pool Sarge a little "nip" to get him to let you borrow the Tubing Cutter and a Screwdriver

Notes:
1) You don't have to remove the bad metal line if it's going to be difficult, just route the Flex along side it.
2) IF the Flex piece is very long, you might use some Tie-Wraps to attach the Flex to keep it from sagging.
3) The make a very small Tubing Cutter, which may be easier to get into place for the two cuts.
4) You're probably going to do the job (depending on the length of the Flex) for under $20.

AND...
THANK YOU for your service to this Country !