Antique pistol refinish advice needed

My brother dropped off with me an antique pistol. A two barreled caplock pocket pistol.
He'd had it in a shadowbox hung on his wall for many years. The pistol itself came from our grandfathers collection of MANY early firearms.
Sadly, the pistol was a casualty of hurricane Ian and had been under salt water and had not been found for several weeks.
Okay, I have used Vinegar & salt soak to loosen the rust followed by wire brushing & have it clean but pitted and showing clear evidence of its troubles.
I know it will never have its original patina or original finish from the early / mid 1800s. What I want to learn is what chemical browning / blueing etc will get it near to what it used to be or at least to be presentable again in a new shadowbox for my brother.
Your advice and experience will be welcome. Photos will be posted when its done. Photos from before I started would bring tears to your eyes so I won't punish you.

Jack, It had very little finish with old corrosion around where the nipples are. It's a lot worse now though, A warm brown finish similar to the other caplocks I have would work for me, I understand that no matter what finish I treat it with, it will always be pitted and have darker spots where the rust had its way. Not trying to make it a fake original, just a display pistol.

Hawg; with respect, have you ever seen a pistol that has been immersed in salt water, then held in a warm wet salty area for several weeks? The wire brush was a toothbrush sized fine wire hand brush not a power tool.