First off, welcome to FTE and congrats on your purchase!

Now, that said:
On your truck, the gas tank should be in the cab. Not sure how it could have leaked into the bed. Maybe it could happen if you have a unibody and a ton of rust in the back of cab/front of bed area. Or an aftermarket tank in the bed.

Next point: your truck is 56 years old. Likely all rubber is shot. That includes flex lines in the brake system. Since you say you don't have much knowledge in auto repair, try to pick up the shop manual (not sure if actually called that) for the truck. You can find them on ebay occasionally.

Once you get the manual, tear into the brakes and do a thorough inspection. Unless it looks like its all been replaced recently, replace anything which is suspect. On something which is 56 years old, that may be everything master cylinder to wheel cylinder, shoes, springs and lines. The brakes are the most important system on the truck! Also, one of the simplest. Once they are in good shape, you will have a good foundation to build upon. I'm not saying it'll be quick, especially if it will be your introduction to mechanical work. Take your time; do it right.


Next:

You shouldn't be smelling fumes in the cab, gas tank or no. It's vented externally. If you are, it's probably the rubber hoses which are most likely disintegrating. Replace the hoses and that should eliminate fumes.

You can add a rear tank if you like, but its a completely custom job. You'll have to rerun the fuel lines, construct some type of mount, and figure out how to fill it. Most of the rear tanks like that require a hole cut in the bed floor, but other options may be available. Once you have the skills mechanically, you can do whatever you like. Especially on trucks like these; they're incredibly simple to own and maintain.

Have fun, and good luck!

 

The fuel filler neck gasket is another piece that can leak.Once it starts to crack, any fuel spilled from filling up or over filling can leak into the cab.

 

 

The rubber grommet (9080 in pic) fits into the hole in the cab, retains the fuel filler tube in place.

The neoprene fuel filler hose (9047) clamps to the filler tube (9034), then to the fuel tank (9002). Over time, it age cracks, allowing fuel vapors to waft inside the cab.

The sending unit (9275) has a cork gasket (9276) between it and the tank. Cork shrinks with age, vapors can waft from it.

The fuel line routes from the top of the tank, over to the left side, then down the left side.

Between it and the fuel line that routes to the fuel pump along the frame rail is a short neoprene hose. If this hose cracks, fuel leaks from it, but not inside the cab.

The thing is, some people overfill the tank, so the filler tube is full of gas, so when this occurs, fuel can leak out if the filler hose is cracked.

But overfilling the tank is the wrong thing to do, because gas expands when it's hot.

So fuel can not only leak inside the cab from the hose, but can seep past the fuel cap, run down the outside of the cab.

 

 

As others have mentioned, if the tank as well as the gaskets and rubber etc are all in good condition, there will be no fumes in the cab. Safety as well is debatable. Some would argue that the tank is better protected from impact behind the seat. Ultimately, it's your decision, since it's your truck. The biggest downside of keeping it behind the seat is making sure to not overfill it. As ND stated, gas expands when hot and can overflow, Also, with a full tank, when parked (with a lean to the left) it can overflow. Both are easy to prevent. Neither of these issues are eliminated by relocating the tank either.


Do you mean underneath the bed? If you are planning to give the appearance of being original, keep in mid that moving 1 thing often affects others. A gas tank relocated under the bed will have you searching for a new home for the spare tire.

 

 

I owned a 1965 F100 for 44 years (1965/2009) and outside of replacing the fuel filler hose once (in 1981), I had no other problems.

IMO, the tank is safer inside the cab than it is behind the rear axle. Having it there caused the Pinto/Bobcat & Crown Vic/Grand Marquis fuel tanks to explode when rear ended.

These tanks (and the 1965/73 Mustang tanks people swap into these trucks) are made from an upper and lower section welded together forming a lip 3/4" around the circumference.

When rear ended, the tank was pushed forward, the lip hit the center of the rear end, causing it to split open. It also caused the fuel filler tube to pull out of the tank.

btw: The exploding Pinto fuel tank fiasco did not affect station wagons, only the two doors and runabouts.