The FamilySearch Research's Wiki's article United States Record Finder gives the following suggestions for finding dates and places of death (and burial, but you may have that already). They separate their suggestions into two batches:
- Vital Records
- Church Records
- Town Records
- Probate Records
- Bible Records
- Military Records
I am guessing that 'newspapers' in the second category refers to articles that are not obituaries. That could include legal notices about his estate, writeups of the funeral, etc. as well as the obituary itself. Think broadly and include 'periodicals' for that second group (employee newsletters, frateral organization newsletters, etc.) as well as newspapers.
You have a cemetery listing, so on the principle of 'start with what you know', try contacting Ligonier Valley Cemetery to see if they have any records. They might have a record of the date of burial (if he is buried there, and the marker is not simply a memorial), and perhaps of the Funeral Home in charge.
If you can find the name of the funeral home, see if they are still in business, or if their records were kept by a local archive or historical society. Records there might include a copy of the death certificate, or give you other clues that would lead you to it. The same goes for the Bethlen Home for the Elderly - do records survive for that period, and if so, which repository holds them?
Check local historical and genealogical societies and archives. Is there a town historian? Were death records kept at a town or county level? (See the Resources list at the bottom of this answer for other indexes you could consult.)
It appears that the Bethlen Home and the Cemetery are in the same county. Could he have died at a medical facility over the county line? In that case, death records might exist in more than one county.
It seems unlikely to me that there would be no death certificate at all, since by the 1960s some kind of paperwork would have been required for a body to be buried or cremated. Find out what the procedures were for that period, and then work backwards from the cemetery to see what you can discover. For a guide to searching Historical Pennsylvania state statutes, see the resources link for Judy G. Russell's post A gift for Keystone State researchers.
In my husband's family, I was only able to find one of his relatives in the Social Security Death Index by searching for the known location of death and her dates. Once I had the entry, I could see that her surname had been misspelled. You may not be able to figure out why you can't find him in the big index until you have the death certificate in hand.
Ancestry's Pennsylvania, U.S., Death Certificates, 1906-1969 can be viewed by browsing. Certificates are filed by number. Sometimes we don't find records in their expected chronological sequence because they are misfiled. We don't know how the indexes were generated, but is it possible that the year of death was misread? Have you tested Ancestry's database to see if there are entries that have no names? Assuming an index is complete is a common cause of not finding a certificate.
Side note: This may not be relevant to your question, but users of Ancestry's 5-year indexes for Massachusetts should be aware that the OCR reading is not perfect. Entries for two people sometimes are combined, surnames get assigned to the wrong lines, entries get skipped, etc. Do not assume your person is not in the index without looking at the original images.
One other thought: this is more likely to happen with a birth, but could his death certificate have been amended, perhaps to correct his name? Amended certificates might show up in a separate index, or not be in the main sequence, or be listed in a year you don't expect. Local historians and archivists, the local historical societies, the local genealogical societies, and local reference librarians would be more likely to know about coverage issues for local records, but you could also try looking in research guides about doing research in the state.
- Some Genealogy Records Have No Names by Crista Cowan of Ancestry, a Barefoot Genealogist video from her Ancestry Desktop Education Playlist
- FamilySearch Research Wiki: How to Find Pennsylvania Death Records
- FamilySearch Research Wiki: Pennsylvania Vital Records
- FamilySearch Research Wiki: Pennsylvania Online Genealogy Records]7
- National Genealogical Society, Research in the States: Pennsylvania
- Online Pennsylvania Death Records, Indexes & Obituaries, a genealogy guide by Joe Beine
- The Ancestor Hunt: Free Online Pennsylvania Death Records and Indexes
- The Ancestor Hunt: Free Pennsylvania Obituaries and Obituary Index Links
- Death in the wrong place by Judy G. Russell, The Legal Genealogist, Jan 21, 2015
- Following up on death by Judy G. Russell, The Legal Genealogist, Jan 22, 2015
- A gift for Keystone State researchers by Judy G. Russell, The Legal Genealogist, Dec 13, 2021