Is the gauge of a circuit a function of the draw, or a function of the distance?
Building wiring must be breaker protected

The first rule is that wire gauge must be sufficient to prevent wire overheating, in all conditions including fault conditions.   So as far as any permanently installed, in-wall wiring goes, 20+A = 10 AWG wire.  15+ amps = 12 AWG wire.  0-15 amps = 14 AWG wire.  You're not allowed to go smaller in in-wall-wiring.  Also, lighting must be derated 125%, so a 13A lighting circuit gets derated to 16.25A necessitating #12 wire. 

And the circuit must be protected by breakers of appropriate sizes.  The only exception is the tap rules, which do in fact allow for luminaires, but don't allow smaller than #14 wire. 

Mains wiring inside fixtures is also limited

Now, with 120V mains wiring, there's a bottom limit on inside-fixture wiring of 18 AWG.  That is the smallest wire size you'll see allowed.  So your 24 AWG tendrils down to individual lamps are a no-go.  

Further, your plan is to fit C9/E17 sockets there.  It is inevitable that some "epsilon minus" type will stick 40 watt incandescents in there. You must design your fixture for that, or, use socket types which prevent this, or don't use sockets at all.  Which segues into...

Low voltage lighting is far less limited

If you want to dodge these design regulations, that's the way to go.  Obviously you will not be using incandescent lighting on low voltage DC, because the voltage drop will require thick wires.  But that means LED, and LEDs in low voltage configuration are so reliable they don't need sockets, which also solves the abovementioned "you must plan for idiots" problem. 

So for instance you might build your horizontal festoon with something like C7/E9 sockets, or whatever... Then have tiny tendrils with a socket on one end, and a self-contained, hardwired LEDs+resistors on the other end.  Given that you want 7W light, that's about 1W of LED light, so 80ma on that tendril @12V or 40ma @24V. 

Your festoon, on the other hand, would need to be appropriately thick to avoid voltage drop, since 12V is very, very sensitive to voltage drop.  It really depends on how many lights you have.  For the festoon, you could simply use a pre-made string of Christmas lights with the normal bulbs removed, and attached to 12V or 24V.