Another excellent suggestion. I'll do that.
I took a look at the government portal for getting service records, but it looks as though I would not be able to get any unit information out of them for some time (requires either 25 years to have passed since death - that'd be 2029 - or family consent to release the information).
It appears that he and Phyllis may have had a son, so I am looking to see whether I can track him down.