I have a 64 Falcon sedan with the "B" pillar.
I have had it since 1964 in my family.
The car in the ad is a hard top which is without a pillar as part of the car. Probably not a Sprint---more desirable than the Futura model which is what it may be. Get both a 1964 Falcon and 1965 Mustang/Falcon shop manuals for very detailed info of the car.
Where the top meets the rear of the horizontal part of the body---by the front of the trunk, there are, on both sides, a welded seam running from the front corner edge of the trunk to the rear window. I have seen these hard tops at that joint split because the car has been hopped up and the torque force of the car "twisting" eventually weakens the weld. That's why a roll lbar is used especially on those hard tops! There may be broken welds & cracks in the welded areas where the shock tower meets the firewall. Watch out for bondo or body repairs..the paint may look good, but watch out for rust eating away the sheet metal & paint later on.
Look for rust in front of the rear wheel wells, where the fierewall ends & the floor pan begins. Look behind the door panels front & back for signs of rust beginning. A the front vents just before the front windshield underneath that area look for rust breaking through where the right heater vent meets the cowl and the same area on the left side. Those 2 areas are known to rust as the owner neglects them when water gets in. Since the owner did alot of mods to the car, look how WELL THE WORK & MODS were done!!!
With only a 302 engine in there, why the battery in the trunk unless he was looking for more weight for better traction. Watch out for excess holes drilled or welded areas done by others & not the factory. Lastly, look at the wires to see if any of them are cut, frayed, missing. Make sure all electricals work!!!!
Try to find out of this was a Calif car or one brought in from anoher wet state like Nebraska or where snow & rain is in excess. This all depends how bad & how much you want the car. Don't think you can fix all that wrong stuff--the idea is to get a car that is sound. It looks like the car has been set up to suit the owner and not you. So keep that in mind as you may want to do something and it can't be done as his work would interfere with you plans.
I would pay no more than $1,500. Figure how much it would cost to fix it after you bought it---if it is repairable and deduct from that price.
Always expect to hear a "good reason rather than the REAL reason" the car is for sale or any other ecuse about the car.
My car is sound, no rust or butchery of the body frame or electrical system. It has a Windsor 427 stroked with Aussie heads Tremec 5 speed and 350:1 rear end with a RRS front coil over suspension that allowed the shock towers to be clearanced for a bigger engine later, rack & pinion and Ford Crown Vic rear discs. There is no upper a-arm to get in the way of the headers. If interested in more info let me know.
Good luck