AFAIK, Hornady does not make 8mm gas checks, I use Hornady 32 cal checks #7080 with 8 mm boolits.
I have easily purchased Hornady checks from both Brownells and Grafs .com.
https://www.brownells.com/reloading/...prod41180.aspx
https://www.grafs.com/retail/catalog...productId/6870
Both are VERY nice to deal with (and will happily special order stuff not normally stocked,) and have VERY good export desks to manage ITAR and other Government Export Regulation and manufacturer’s agreements.
Grafs informed me that gas checks are specifically excluded from ITAR and other Government Export Regulation.
(AFAIK, there are no ITAR or other Government Export Regulation of reloading or bullet manufacturing tools such as molds or swaging tools, and no restriction on lead wire for swaging jacketed bullets. I do not know if there are restrictions on export of jackets for bullet swaging, (gas checks are just short jackets).)
Lyman also makes gas checks, that are designed to fall off in flight and not crimped to the boolit base like Hornady.
‘Gator checks’
http://castboolits.gunloads.com/show...tor-gas-checks
http://www.go2gbo.com/forums/99-ask-...ks-source.html
http://www.lasc.us/CheckShankSize.htm
http://www.dragonbulletlube.com/products.php#gasChecks
‘Freechex’
http://www.freechex.net/
sell punches for forming gas checks from sheet copper or aluminum beverage cans, (AFAIK they are the Lyman non-crimp design).
I have not tried them, but aluminum beverage cans are thinner than Hornady copper, (some report using a double stack).
Some bullet makers (such as BDX,
http://www.canadianbdx.com/) form their own jackets and have scrap copper jacket sheeting suitable for punching gas checks.
A google search will find many more similar.
https://www.patmarlins.com/
https://www.patmarlins.com/product-category/checkmaker/
If you are loading for a military Mauser with a typical long throat and fast twist,
a custom mold designed and part of a castboolits group order is available from
https://www.midsouthshooterssupply.c...roduction-mold
My results were VERY good, and MUCH more accurate than the std Lee 175 grain boolit.
https://mauserloader.wordpress.com/2...er-experiment/
http://castboolits.gunloads.com/show...for-8mm-mauser
Good Luck, YMMV.