Brake Lights not working.

[Spool]

Rings Removed.
You are absolutely right, brake lights work on battery power.
For the longest time, I was within the belief that brake lights didn't work with the ignition off.

I cleaned and sanded the fuse sockets and replaced all the cartridge fuses. Brake Lights work!
They didn't however work when I used a 15 amp fuse as specified in my service manual.
They didn't even work when I used a 20 amp fuse as specified on the print of the fuse panel itself.
They lit up once I used a 25 amp fuse.
Any idea why?

In the same vein of fuses.
The fuse amperage specified in my service manual has some inconsistencies compared to what's printed on the actual fuse panel.
For example, the accessory fuse (I) (which is currently my brake lights) is a specified above.
My Radio & TCS fuse (D) is 3 amps in the manual but 10amps on the fuse panel.
Which do you think I should abide by?

Thanks to your help, the brake lights work and I think my next move is cleaning the Bulk Head connector and Fuse panel which will also allow
the rest of my wiring projects a bit of ease.

Del City offered me free shipping on my first order, which is great considering they charge $15 to ship terminal connections.
I'm currently ordering
-Female Spades with Locking Pins at 16-14gauge and 20-18gauge - (10 of each)
-Male Packard Type 56 Terminals at 16-14gauge and 20-18gauge - (10 of each)

Any other connections you think I could order ahead of time if cleaning up most, if not all of my wiring is my goal?

[bd]

I cleaned and sanded the fuse sockets and replaced all the cartridge fuses. Brake Lights work!
They didn't however work when I used a 15 amp fuse as specified in my service manual.
They didn't even work when I used a 20 amp fuse as specified on the print of the fuse panel itself.
They lit up once I used a 25 amp fuse.
Any idea why?   
There is still a connection issue at the fuse box - possibly behind the fuse box.  Check for oxidation of the fuse box brass buses, terminals and rivets.  Or, less likely, there may be an intermittent open in the wiring.

In the same vein of fuses.
The fuse amperage specified in my service manual has some inconsistencies compared to what's printed on the actual fuse panel.   
Install fuses as indicated on the fuse box.
For example, the accessory fuse (I) (which is currently my brake lights) is a specified above.   
(I) is B+, not accessory.  The accessory fuse is located near the lower left corner of the fuse box, (D) above the turn signal flasher.  Inspect behind the fuse box and figure out why the original orange ckt 40 was abandoned.  Then relocate the brake switch feed to the correct fuse (B), if possible.  Brake lamps should be protected by a 20-amp fuse.
My Radio & TCS fuse (D) is 3 amps in the manual but 10amps on the fuse panel.   
Install a 10-amp fuse.
Which do you think I should abide by?

Any other connections you think I could order ahead of time if cleaning up most, if not all of my wiring is my goal?   
Beyond antioxidant and the other materials previously discussed and recommended, only you can answer this question after careful inspection and inventory.