A thought from a resourcing standpoint: instead of a full on new player faction with its own NPC's, dialogue, quests, etc, it would probably be a much simpler matter if a similar solution could be done with as little development time and effort as possible via pre-existing assets. Eg, instead of design new armor for the neutral faction, copy the stats of a faction restricted armor, remove the restriction, and use a different cosmetic asset. Or in stead of blocking access to higher rebel/empire goodies, the neutral mercs can for example during a temp-join of the empire do the participation in empire stuff but their rewards are lower due to a "disloyalty" penalty. That's basically what Boba Fett did; and I think a lot of people want to be a badass bounty hunter, but it'll take more work to get FancyArmorSet1 as a neutral than if you were directly rebellion or empire.
Or, alternate solution, relatively-simple bounty and temporary allegiance quests available for neutrals, or use existing assets to help make a reputation faction for neutrals and throw neutral players into fights with either rebellion or imperial depending on which is in need of a population boost.
...anyway, resourcing aside, it makes lore sense for a neutral to want to have some affability for one faction or both but generally be free to go about their own interests. Eg, maybe you want to do some naughty experiments to make a cyborg-mech-acklay to put in your palace some day when you're rich so you have something more original than a rancor, and the rebellion is going all "your research is un-ethey-kaaaal! Stawhp!" so instead you do business with the empire, not necessarily to get access to imperial goods per se, but so that they look the other way on your activities (something akin to the empire's arrangements with the hutt cartel).
Or, vice versa, suppose your interests are more political. You have beef with a local imperial governor for whatever reason so the rebellion becomes an ally of convenience; let's say you have a financial stake in a weapon's manufacturing company that the empire is regulating a bit more than the rebels have the manpower and capability to, so you buddy with the rebels because you find it more viable an economic investment for this weapon manufacturer on that planet and the rebels are a more manageable neighbor.
A neutral mercenary could have any number of ulterior motives. That, and a lot of people probably want to be an awesome boba fett and own their own big shiny things some day. Possibly some city-building benefits / construction and town perks could be designed to help provoke that kind of backdealing.. though that'd be its own resource discussion altogether.
A lot of interesting ideas. I do think you are onto something about having a neutral faction that temporarily aligns with one of the two major factions. Having a third, separate faction just isn't realistic from a design standpoint. Too much of the game would have to be revamped. However, it would be practical, depending on who you are and what you are doing (bounty hunting, smuggling, etc.), to allow someone who is neutral to align with one side or switch between them based on the circumstances.
That is far more manageable and could lead to some interesting dynamics within the game as players that are committed to one of the two main factions would never know if the neutral player can be trusted. It's definitely something I think the dev team should consider once the game has been released, the final patch of the game has been implemented, and they are looking at adding new content. There are a lot of possibilities with this approach and it would be interesting to see how it works in practice.