These were the earliest examples of bondage cover art images, and ran from about 1910 (when the pulps became more common) until roughly 1975 (when the "Men's adventure" type of magazines started to disappear).
Perhaps the earliest detective magazine to employ photographic covers was "Actual Detective Magazine," whose first issue appeared in November, 1937. The earliest use of a color photo on a cover is the February 1939 issue of True magazine, with the February 1940 edition apparently the first to feature a gag worn by a damsel in distress. The peak era for these was the era from roughly 1959 until 1986, when, due to the Meese Commission (a contribution by Park Dietz), and the end of a few of the publishers of Detective (or "True Crime") magazines, the main era of the bondage cover ended, though there were a few issues of Detective Dragnet in the late 1980s and early 1990s, and a brief revival from about 1994 until 2000, though even then few and far between (unlike the late 1960s, when at least 2 such covers could be seen monthly. Also, the use of over-the-mouth gags was common enough that the slang term "Detective gag" is used for it.