From The American Woman's Cookbook:
4 eggs, separated [Beat whites until stiff.]
1/2 cup whipping cream [Whip until stiff.]
4 Tablespoons brandy or whisky [or rum].
3 Tablespoons powdered sugar
Beat the yolks till thick and lemon colored.
Slowly beat in the brandy and sugar.
Fold in the stiffly beaten whites and the whipped cream.
This must be eaten with a spoon.
By not whipping the egg whites or the cream, the mixture would be a thick liquid and is probably the eggnog I remember from the 1950s and early 1960s.
Here is a link to that recipe in the cookbook, page 757:
There is another recipe for eggnog on the page which calls for beaten egg whites and milk, just below the one for Southern eggnog,
and also one for children on page 648.
When I was young, the children got eggnog made with cream, milk, egg yolks, sugar and vanilla.
ETA: One could substitute a "tea" made from stevia leaves for the sugar, or simply leave it out.
Hope these are of use to you.