I'm not for sure about the 'exact' proceedure for your 1962, but on my 1975, it goes as follows and is not too hard of a job.
Hopefully this is close to what you are looking at and not way the **** out in left field chasing a tornado.
*you will want to have another set of hands for parts of the process, but it can be achieved solo with proper positioning of your tongue in your mouth and uncomfortable contortion of your body's appendages*
1. Disconnect battery
2. Remove gas cap and siphon gas from tank (tank is pretty light when empty)
3. Remove gas fill cover
4. Remove gas fill overspill 'cup' from around tank filler neck (be careful not to make any debris in the cup fall into tank while removing)
5. Replace gas cap to help keep debris out.
6. Disconnect electrical wires from top of tank
7. Remove spare tire carrier assembly
8. There are 4x bolts on the forward crossmember holding the tank in place, 2x on each side. *I did not touch the rear crossmember tank support*
These are true nut and bolt type fasteners.
There is a hole on the outside of the frame to stick a closed end wrench into the frame and hold the bolts from the top.
It may be very tough to get to the tops of these bolts in the frame while under the car removing the nuts, you may need 2x people for this part.
9. Once the bolts are removed, the crossmember should slip towards the front of the car and allow it's removal from the straps going over the top of the tank.
Once the cross-member is out of the way, either by moving it far enough or total removal, the tank should drop until it hits your exhaust system.
*you should have enough fuel line slop to allow this 4" - 6" drop, another set of eyes up top watching them while you are lowering the tank would be worth any money for peace of mind, lol
I had enough slop on fuel lines, but not on electrical personally, hence step 6 above*
*This gives about 4" - 6" to work on the tank to replace fuel lines and/or clean the electrical contacts from the top.
NOTICE the crossmember orientation and bolt holes, ie, take a picture before you remove the forward crossmember.
On mine, one side was simple holes, and the other side was slotted holes to allow some slip when attaching.
...If you need to totally remove the tank from the car, you will probably need to remove the rear portions of your exhaust system.
Therefore, the removal of the exhaust should be before you totally remove all bolts from the crossmember.
To re-install the tank, it's pretty much a reverse of the disassembly, but I will add a few notes from my experience.
Make sure to replace the gas tank vibration strips on the crossmembers, both front and rear if/when they disentigrate when removed.
They are cheap so it might be a good idea to plan on replacing them anyway if they are original. The ones on my car fell apart when I removed the tank, soooo
After I purchased mine, I read about peple using home-grown replacements like the roofing paper that goes under the shingles on a roof, whatever it's called, with great success... ymmv
You can attempt to bench-press the tank manually with muscle, or stick a jack under there with you and let the jack do the muscle.
I had person 2 hold the top of the tank and guide it into position while I pushed it in from the bottom, I imagine you could do it by yourself, but I don't know how it would go as I had help 'spotting' up top.
At any rate...
Push the tank back into it's hole and then attach one crossmember bolt on one side loosely (the side with simple holes).
Then pry the crossmember back into place under the tank and supporting it and get another bolt started on the other side (with the slot holes for slip).
Once you have both sides loose but started with one bolt, install the remaining two bolts loose, make sure the vibration strips are in place correct and then tighten all 4x crossmember bolts.
Have fun, and welcome!