patterns
I patttern my turkey guns on a standard sheet of printer/copier paper....8-1/2 x 11 (?)". On that sheet I hand drew the resemblence of a gobblers head and neck, more or less centered on the page. I staple the page to a standard sheet of newspaper. I copy the drawing now and again on my printer, so I have the same target from year to year. The big sheet of news print lets me see if the pattern is centered more or less overall, the sheet of printer paper lets me get specific.
I think turkey gun patterns are better evaluated by how many pellets will land on that sheet of paper, than by counting individual pellet holes in the turkey shape. Oh, I count the holes in the shape, but that count can vary by as many as 10-12 pellets or more. But counting the page gives me an idea of how dense the center of my pattern is, shot to shot, for various loads.
The larger, more consistent target SHEET, is a better measure of what your gun is doing.
Alpha, your turkey head may be slimmer or fatter than my rendition, yielding different pellet counts, but a sheet of standard paper is universal. If your turkey target is on a standard page, what is the pellet count on the PAGE? Your count of 10-12 pellets on the target is a bit hard to compare, but a page count will be useful against my own experience, as follows:
When I was using my Grandad's vintage pump gun (1921 model, 12 ga full choke, fixed of course) ) and 1-1/4 oz of #6 from standard lead field loads, the old gun would avg about 65 +/- pellets on the page, and land about 20 +/- on the head an neck. The best shot I got with it was 72 on the page and 25 on the shape. I deemed that enough gun ( in 1975 it was my ONLY shotgun), to hunt gobblers, and killed my first couple with it, but both were inside of 35 yds. I doubt my first bird was over 25.
I'd hazzard to estimate, that if you are getting minimally 50-55 pellets on a sheet of printer paper at 30 yds, you have enough gun for shots to distance 30-35 yds. Your count of 8-10 pellets on the head/neck is variable as I mentioned, and I would like to see it a bit higher, but the page count will tell me more.
UNderstand that you are a long way from what a dedicated turkey gun will do, and will have to limit your range accordingly. My two serious turkey guns, 12 ga with 3" loads and 1-3/4 oz of #5 lead shot from the new Win "XR" loads, will consistently put over 200 pellets on a sheet of copier paper at 30 yds. My old load, the Win Supreme 1-3/4, #5 lead, will put 180 on the page. With those loads, I can cleanly kill a gobbler at 45 yds +, but really try not to shoot that far if I can possibly help it. To deliver the ultra dense patterns from those guns on target, (head and neck) rifle sights, a dot, or even a low powered scope are very important. You will not have that issue, but you will have to be very careful with your range not to exceed 30-35 yds, and closer is better.