If the police confiscate a weapon that isn't owned by the suspect,
would they have grounds to keep it?
Not forever.
For example, let's say the gun was owned by a friend or parent? What
if the gun was owned by a Trust with several trustees?
Third party owners of property lawfully seized from someone else can recover it.
For example, I once took legal actions to recover a gun for a client that was in a gun repair shop that was seized in a criminal investigation because most of the inventory of the shop where it was being repaired consisted of stolen firearms and the primary business of the gun repair shop was fencing stolen property (a fact of which my client was completely unaware and shocked to discover). But, that was only possible once the trial was over because the guns seized were part of the evidence in that trial.
A similar process applies when there is a civil forfeiture of property owned by a third-party.
Could the owner (personal or trustee) recover the gun from police
custody independently of a court finding on the suspect?
Sort of. But it isn't entirely independent, since the firearm might be needed as evidence or might need to be kept out of the possession of the person from whom it was seized to effect the red flag order while it was in place in a way that that the third-party owners would have to assure.
An example might be where a gun is confiscated via red-flag law, where
no crime has been committed, but the suspect won't get his day in
court for 6 months. Would the true owner, or partner owners if in a
Trust, be denied their property or could they go ahead and recover it
pre-trial (ie. the day after it was confiscated)?
In the case of a red-flag seizure, the existence of the gun wouldn't be evidence in the court proceeding, so it wouldn't have to be retained for that purpose prior to trial.
But, the owner of the gun would probably have to petition the court to regain possession and would have to demonstrate that the red-flag order would continue to deny the person who had the gun possession of it until the red-flag order period expired (if ever).
If the trustee was the red-flag order target, or was someone related to him (or her), that might be a showing that the trustee could not make.
Caveat
Of course, red-flag laws are specific pieces of state legislation. Each one is different. Many would provide a specific statutory procedure for how this issue would be handled.
For example, in some places, the proper means to regain possession of property held by law enforcement in connection with a criminal case is a motion filed by a third-party intervenor in the criminal case, while in others, the property process is to bring a civil action for replevin (a lawsuit to regain physical possession of particular items) against the law enforcement officer in possession or constructive possession of the property in question.