3-ways and 5-ways - Deaf Eddie

Here's a drawing I’ve done that might enlighten - a side view of a 3-way/5-way:
This is ONE POLE, remember - it's repeated in mirror image on the other side of the
switch. You can see that the common lug is always in contact with the wiper, and the
contact point on the wiper moves across the switchable lugs as you work the lever.
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You have to fully grasp the concept that your 3-way (or 5-way) is really TWO separatebut-parallel-and-synchronized
switches.
In Strats and Teles, the jumpers between the two poles (wires that cross over) are
simply to connect the results of those TWO separate switches. It is then sent on to
the volume pot.
In the case of the stock Strat, with the two COMMONS jumpered together, it's because
one pole runs the pickup selection, and the other pole runs the tone control selection.
Now, they could have just connected both commons separately to the volume pot - yes,
they could have run two wires meeting at the volume pot, using NO JUMPERS - and
achieved the same thing.
Jumpering them together across the switch is just a "shortcut" to have both the tone-potsside
of the switch and the pickups-side of the switch connected to the volume pot with the
minimum amount of wire.
They don't really HAVE to have any lugs jumpered together, there's no circuitry magic -
it's just a wiring shortcut.