Trunk hardware

can you tell what kind of tire do you have that will fit there and allow the flat cover to fit flat in the trunk? It's gotta be a pretty thin tire I guess...
Don't know what they used for that commercial.
The one in my car is an E78-14, and the biggest offered new in '67 was D78. Later E70 was offered but not sure how the sidewall to to sidewall width differed, if at all. The E78 sits a little higher than the floor.