That originally specified "6.00x13" would be six inches wide, or almost 155 mm, so it would be roughly a 155/xx-13, where xx is an aspect ratio of 78 or more; the spare is likely a near match for the original size. An A78-13 would be about the same size, while a B78-13 is closer to the 175/80-13 which Bill mentioned. The 185/80R13 is definitely bigger than stock.
I think bigger than stock is appropriate, just as modern cars use much wider tires and larger diameter wheels than the cars of the 1970's to suit modern driving conditions and expectations, and people improving 1970's cars (not stock restorations) put bigger tires on them.
The "ST" designation before a modern size (e.g. ST175/80R13) or on the end of a "traditional" size (e.g. B78-13ST) means Special Trailer; it's that designation, not the size, that indicates that a particular tire is specifically for trailers. I really don't think ST tires have any new technology; instead, it is the Passenger (P) tires that have advanced. There are lots of discussions in this forum of ST versus P (and versus LT and commercial) types of tires; the subject of sizing (including the use of lower aspect ratios) appears in the same topics.
1979 Boler B1700RGH, pulled by 2004 Toyota Sienna LE 2WD
Information is good. Lack of information is not so good, but misinformation is much worse. Check facts, and apply common sense liberally.
STATUS: No longer active in forum.