As to how the aux (added) tanks were managed in the Electra, I'm not sure. Sometimes aux tanks like that are allowed to run down to point of 'sputter' - with a watchful pilot watching the time, from good altitude. Gary LaPook has hands-on experience with that over the ocean in single-engine airplanes (and maybe others) - I'm sure he can share some insight.
I always took off on the main tanks because I figured those tanks might be a little bit more reliable than the ferry system. At a safe altitude I would switch to the ferry tank and use it completely, saving the mains for the final part of the flight and landing. Here is
a link to a story showing that this is a good method. If I had saved that ferry tank til the end it would have been THE END!
Often such extra tanks are also used to supply normal tanks periodically, until dry: fuel is moved from the big tank out into a 'normal' permanent tank, as needed, thence consumed by the engine(s) from the normal source. I do not know how the arrangement worked on the Electra, however.
LTM -
The Electra did not have fuel gauges for the cabin ferry tanks so, in order to avoid
that embarrassing silence since both engines would quit at the same time because they were both drawing fuel from the same tank, Earhart would burn each ferry tank to a conservative point, based on her clock, and then switch to another tank. This left some fuel in the tank she had just finished using which is why a "stripping system" was included in the fuel system. After switching tanks, by manipulating the "stripping valve" and then using the hand operated "wobble pump," she would pump that remaining fuel into one of the main tanks to be used latter. This is another reason that you have to use the mains first, to make room for the fuel that will eventually be "stripped" from the ferry tanks.
I believe there is a diagram of the fuel system somewhere on the TIGHAR website. If not then you can find it at Purdue.
gl