From your pictures your car looks to have the orginal engine still in it. To verify this looking at the right front top corner (just below the head deck) of the engine block there will be a flat boss on all 1960 to 63 engines. That will have either an N stamped in it code for a 144 six or a T code for a 170 six. The Casting / Design numbers and a Date Codes are also cast into the major parts like block, head, ect. The head number is right on top of the intake log next to the carburetor. You if you are planing to restore your car to Factory Original I wrote a post on the correct engine colors Ford the sec for these early six'es too see below link. Something else to do that is almost free and can have a big effect on a car that has sat unused that many years is to clean up the electrical and ground connections really well on the car so that they are all good snug contacts. If your engine is an original 1962 it will have a solid lifter cam. Have you checked the Hot valve lash or done valve lash setting yet? Have you done a compression test yet? If so what were the results?
Here is info on how the stock Load O Matic (LOM) distribitor works too.
https://fordsix.com/ci/Loadomatic.html
Here are the Stock 1962 144 or 170 Tune up specs
Distribitor rotates CW firing order is 153624
Autolite BF-82 plugs gaped at .034.
Basic Points setting gapping them at .025 but for the very best performance your looking for a Dwell setting of 37 Degrees.
Base timing is set to 4 Degrees BTDC for a Standard ( Stick) trans and 12 Degrees BTDC for a Automatic trans.
Idle RPM is 550 to 600 RPM for a Standard Trans and 500 to 525 RPM with an Auto Trans in Drive, parking brake set,
Fuel pressure is 4.5 PSI
To get most accurate tune up with a orginal point ignition always use of a tach / dwell meter, and also a timing light. This is the procedure I have used for decades to quickly do a precision tune up.
A good tune up follows this order of work.
1. Set the plug gap to .034
2. Set the points basic setting to .025 after its running set the Dwell Angel to factory spec of 37 degrees.
3. Now you need to set the timing to the 6 degrees (with stick Trans) or 12 degrees (Auto Trans) base timing vacuum line disconnected and plugged. You can also try more base timing to as much as 16 degrees but if there is any hint of pinging when you try it driving it up a slight grade then back it off until it stops. Reinstall the vaccum line to the Distribitor after setting the base timing.
4. With engine warmed up good, the intake and exhaust valve lash is set to .016 hot.
5. With warmed up good and the choke blade is fully open too. Set the Idle mixture to its Lean Best Idle. ie set to highest idle RPM then turn the mixture screw in 1/4 turn to lean it. See Addistional Notes below.
6. Set the curb idle speed to 550 to 600 RPM if standard Trans. Set idle RPM's to 500 to 525 RPM with an Auto trans in drive parking brake set, wheels chocked with block of wood, or you can have someone set in it and hold the brakes.
7. Repeat 5. & 6. To see if it improves anymore. When properly tuned these engines (when warmed up) will restart without even touching the gas pedal.
Addistional Notes
You might also test your coils output with the volt / ohm meter to see that it's within spec. Or you can do it by watching the spark color (a Bright Blue) and the lenght it can jump to cap terminal (from 1/2 inch or more).
While doing the tune up settings to the carb mixture and curb idle setting the engine needs everything installed and hooked up just as it will be operated! This includes having the Air Cleaner with a clean air filter installed and the PCV hooked up if your engine has one. If you want to use a Vacuum gauge then hook that up to the Intake Log below the Carb you would be looking for about a steady 17 inches of vacuum at idle RPM. Good luck in your tuning. A good upgrade for these engines is a Pertronix Ignitor engine still looks stock but gives you a hotter spark. Good luck
Ford Six Early Engine Colors
viewtopic.php?f=1&t=77044&p=594605&hilit=Engine+colors#p592955