According to this vintage guide to banana ripeness, for this recipe you should use a banana with a skin that's flecked with brown.
1956 recipe from old Jell-well advertising
Prepare 1 pkg. of Jell-well Vanilla Pudding and Pie Filling according to directions on the box. Allow to cool. (If you prefer, use Jell-well Vanilla Instant Pudding prepared according to directions on the box.)
Line the bottom and sides of a low 9″ square dish with Jane Arden Vanilla Wafers. Cover the wafers with banana slices. Pour half of the pudding over the bananas. Add a second layer of wafers, bananas and the remaining pudding. Chill about 1 hour.
For an extra-special touch, top with whipped cream and sprinkle with crushed vanilla wafers — or make a meringue topping and brown lightly.
Recipe via Click Americana