Although not a Parker shotgun, my Staff Assistant many years ago was on the search for a wood cook stove.
She had many found memories of her grandmother cooking on the stove in El Paso Texas. She tried to find out were it went but no one in the family could recall where it may have gone. She had a picture in her minds eye of it and did some research and found it was a pretty common Maker, Glenwood as I recall.
It took some searching but eventually she found one in El Paso. It was purchased and the professionally restored, including rechroming some pieces.
She never cooked on it but it but it sat beautifully in her ranch style home in the family room.

As suggested already join PGCA and as a member advertise you are looking for a VH made in 1908, you might find a 16 gauge made that year that was delivered in the local vicinity.
Moraima always referred to her stove as her grandmothers stove. Maybe it was but most likely not but it satisfied her desire and brought back great memories for her.

Phil

I had a similar experience with a gun, one which actually never existed.

When my dad was young (11 years old in 1926) he lived on a dirt poor farm with his 12 siblings. He badly wanted a rifle to hunt rabbits and squirrels. Ammo was 1 cent/round at the general store. He decided to sell Rosebud Salve to his neighbors who were as poor as they were. He worked all summer while not working on the farm, walking and selling salve in order to win a Stevens Boy's Rifle. At the end of the summer he completed the order for the several cases he needed to sell and sent in the order along with the collected money. The orders arrived and were delivered. He waited and waited, but his rifle never arrived.

The first year after I graduated from engineering school, I located a mint condition rifle of that model. When he unwrapped the rifle at Christmas, I saw my Dad break down in tears for the first time in his life. He sat and held it for an hour after opening. Often you can't over estimate the importance of some of the memories in your life.

Great story and gesture on your part Art.

Art that was a good thing you did, I am sure that the memories came flooding back to your dad, brought back some memories of my own, as a kid I collected the coupons of Tube Rose Snuff, and could trade them for things in their catalouge Shame on the Rose Bud Salve folks, Gary

That 16 gauge could still be with a family member. As others have mentioned, your family might be your best shot at finding out what happened to the gun. Do keep us posted about your quest.