Suissesse translates to "swiss" in french, naturally this makes it a difficult drink to research. Swiss style absinthe was used in absinthe cocktails, so more formally this drink should be ordered "absinthe suissesse cocktail". However, this drink is no longer prepared in it's original historical form. The suissesse is a direct derivative of the absinthe cocktail.
Brennans placed advertisements in the following publications from 1964 - 1980
New Orleans: a guide to America's most interesting city - Page 135 by Thomas Kurtz Griffin in 1964 Texas Monthly - May 1977 - Page 142 Vol. 5, No. 5 ..Texas Monthly - Feb 1978 - Page 44 Vol. 6, No. 2 Texas Monthly - Apr 1978 - Page 62 Vol. 6, No. 4 Texas Monthly - Mar 1978 - Page 49 Vol. 6, No. 3 Texas Monthly - May 1978 - Page 69 Vol. 6, No. 6 - Texas Monthly - Jun 1978 - Page 68 Vol. 6, No. 6
The suissesse is mentioned by famous authors like Bram Stoker and infamous bartender Jerry Thomas and also by Trader Vic in Bartender's guide - Page 345 by Trader Vic in 1948
"SUISSESSE— 1 1/2 oz. Pernod or Herbsaint 2 dashes orgeat syrup Shake until shaker is frosted; drip through absinthe dripper into chilled highball glass. Drip seltzer until glass is full. Stir gently and serve with straws."
This drink is still served frequently in and around the greater new orleans area. It is difficult to determine an accurate timeframe associated with this drink. As of the late 19th century it contained the following
Absinthe (1 oz.)
Creme de almond
Shake and strain into an empty fizz glass, top with charged soda.