Wild encounters boosted by abilities only apply to the first Pokémon regardless of faint or not, and regardless of the second Pokémon’s ability or not.
Every source I can find specifies the lead spot, and say nothing of the rest of the party. This implies it is, in fact, only the lead spot. Therefore, Static and Synchronize cannot work at the same time, sorry.
I’d recommend just using static, or Masuda Methoding with an everstone.
If the mother (or Ditto) is holding an Everstone, the baby has a 50% chance of inheriting the mother's Nature.
Source
This takes place of the Synchronize, while MM increases the shiny odds significantly with a 100% Emolga Rate.
Now for all the references, I've dug up that support my theory.
Static - Lead spot: 50% higher chance of encountering an Electric-type wild Pokemon.
https://gamefaqs.gamespot.com/3ds/187276-pokemon-sun/answers/457993-overworld-abilities
Overworld Effect:
If the Pokémon is in the leading place in your party, chance of encountering an Electric-type wild Pokémon increases.
https://www.serebii.net/games/ability.shtml
From Pokémon Emerald onward, if a Pokémon with Static is in the first place in the party (even if fainted), then there is a 50% chance the game will force an encounter with an Electric-type Pokémon, if one is possible. As of Pokémon Sword and Shield, it shares this effect with Lightning Rod.
https://bulbapedia.bulbagarden.net/wiki/Static_(Ability)
