A short history of external tanks with the F-35 program re: what would be qualified as stores at the end of SDD.
The original assumption is that they would use legacy F-18 tanks like the conventional shape shown above.
Once they got into simulation and later wind tunnel models doing stores separation they ran into problems. The conventional tank showed to be high risk for bumping into the aircraft and/or other stores.
So they came up with 3 elongated tear-drop designs. (see the graphic in the Sep 2006 brief). These carried a bit less fuel but were supposed to offer a solution. However in the same kinds of simulations there were still problems. There is a brief out there somewhere that shows quite the pitch-up of the tear-drop design coming way too close to the aircraft after being punched off. There were still risk issues of external store separation scenarios; for example when also carrying a 2000lb bomb on the nearby station. Of the three elongated tear-drop candidates the one that showed the most promise was one that had an extension on the pylon.
Eventually they decided that there was too much risk/time/money invested for now and pulled external tanks from SDD as per that April 2006 contract which also removed WCMD (for instance CBU-105). And of course that same contract added SDB for SDD.
Interesting about that April time line as they seem to have had no problem putting tear-drop external tank shapes in the Sep 2006 brief.
Also interesting is that the Norway briefs don't show the range advantage stated by AC above with the unproven external tank mission configuration.
Not long after; briefs started touting the idea that you don't need external tanks compared to legacy.

I am sure that went to the plus side for MX calculations too as you don't need extra people/manhours to clean and maintain external tanks on a deployment if your jet can't carry them.
Maybe we will see them someday after SDD. Who knows? We do know that they have a heck of a lot more important problems to take care of than external tanks right now. Just not a priority.