That depends, on surface ships the helmsman is typically an able seaman in the merchant navy or an designated seaman or petty officer in the Boatswain's Mate community. So during the TOS/DSC-era this would make sense.
On the other hand, during the ENT and TNG+ era, the helmsman function is also typically shared with the Navigator, which is usually a senior enlisted officer (Chief) or a junior officer (in which case they may be dual-hatted as Conning Officer/Junior Officer of the Watch [2-i-C of the watch team]), so the position being held by an officer (though not generally a member of the senior staff).
Second Officer or Third in Command, not third officer.
I think any members of the senior staff that are Bridge Officer qualified wearing "command" makes sense, likewise any other senior officers that stand Duty Officer shifts.
There's some basis to that.
I'm something of a fan of red (technicians), yellow (specialists [Security/Intel, Bridge], white [command], green/teal [Sciences], cyan/blue [Medical, Admin and JAG], but YMMV.