The colour of Briggs engines depends mostly on when they were made. Orange is probably correct for mid-1970s. A lot of them were white in the late 1970s and black in the early 1980s, but orange seemed to turn up on some engines for quite a while before black took over completely.
I suggest you check the condition of the cutter idler pulleys and spindle bearings. Chances are something caused the clutch to wear out and the belt to disappear, and it makes sense to find it and fix it before it all happens again.
