I'm also curious about the Veterans Administration National Cemetery. Is burial in a tribal veterans cemetery included in this information?
This information is for VA national cemeteries.  The other cemeteries provide their own information.
How would I apply by mail?
You would need to fill out an Application for Pre-need Determination of Eligibility for Burial in a VA National Cemetery VA Form 40-10007 and sign it.  You would sent that completed application with copies of your supporting documents to the National Cemetery Scheduling Office in St. Louis.