Ohio? Look very closely for any rust. If it has a new or fairly new paint job then it's very likely that they bondoed over rusted out body panels and then painted it to hide that fact. Like At said: on any high performance vehicle, it's very likely to have run hard so check everything very carefully. If you're not knowledgeable on these models and a knowledgeable mechanic then you should take it to someone that qualifies and pay them to check it before you buy. 100,000 to 120,000 miles is a LOT of miles on a HP vehicle that has been driven hard.
The Fuel Pump Control module is located under the bed of the truck and they have an aluminium housing which is prone to corrosion and rotting out and then leaking dirt and water into the module and killing it. It's not THAT hard to fix, after you know what the problem is but you might want to take a look at it . The back bottom corners of the cab are also very prone to rusting out. I would definitely check them closely. Water getting into the channels under the doors and then rotting out the copper INSIDE of the wires and causing all sorts of odd electrical problem has also been a big problem area and finding the bad wire can be very difficult so look for signs of water damage and/or rust in the door channels. With the massive amounts of wiring and electrical modules in the late model 150s water intrusion anywhere in the cab WILL eventually led to serious problems. Look under the dash, around the windshield, around the back window, around the 3rd brake light, etc ANY signs of water damage or rust.
I'm not sure about the 2013 and 14s but generally all the F-150s of that time frame have problems with Fuse F2. The basic problem is that one of the two contacts in the fuse block that F2 plugs into is a bit too loose and it starts arcing and burns up that spot in the fuse box and sometimes F2 as well. Just to make it clear, F2 doesn't blow, it burns up on one end. F2 supplies power to the fuel pump so usually the first thing that the operator notices is that they try to start the truck and everything appears normal but the truck simply doesn't start. What has happened is that F2 and it's contact(s) have burnt up and the fuel pump isn't getting power and and the engine doesn't get any fuel. Ford (and others) sell F2 relocation kits to repair/elimenate the problem but you can go into the fuse box and clean and tighten F2 and it's contacts and prevent the problem from ever happening. But while you're looking, pop the cover off of the fuse box (under the hood and directly behind the radiator) and pull F2 and see if one end looks burnt or the area that it plugs into looks burnt. Again, it's an easy fix, but only if you're aware of the problem.
beat out of it as well...