Does anyone know how to find records when the person never went to war?
You should still be able to find a service record. I recently found two records for a gentleman who was posted to the Northern Territory with the Army in WWII, but never served overseas. It was a very limited record, mostly of minor medical issues, but a service record no less.
Does nothing come up in the Name Search section of Record Search?
I suspect that 1966-1968 might be a bit too recent for the NAA. The Defence Archives might have that information, but be aware that:
“Third parties requesting access to service records will require the member's authority. For more information see the request for service records form.
Should you be seeking access to a deceased member's service records, please be aware that the applicant will be required to provide proof of relationship such as marriage, birth and death certificates.”
I've contacted the ADF to see if they can put me in the right direction. You may be right about them being too recent, I hadn't really thought about that, because my dad passed away 8 years ago.