You do realize that 13″ is the diameter, not the width…
In any case, you’ll have difficulty finding 13″ tires in any size, especially those tall enough to look good on this car. The closest modern size to original will be something like a 185/80-13. Unfortunately, the only tires you can find in this size today are trailer tires.
On my 1962 wagon, I found a set of 14″ aluminum slot mags from a mid-1960s six cylinder Mustang, which uses the same 4 x4.5″ bolt pattern. I run 195/70-14s (24.75″ dia) on the front and 205/70-14s (25.3″ dia) on the back with no clearance problems at all.
Maxxis makes a great off road 4 wheeler tire. I never used them but many of my race buddies did and all loved them. As long as it crosses over to there on road tire they should be nice. I don’t know where there on road tires are made but the off road tires are not in USA.