When do I know that it’s done?

You could totally do temperature; the author says the toothpick just won't come out clean, not that it'll cause problems with the cake.

How nice to see Elizabeth David's name mentioned!
Anyway, here's an article with 5 ways to test a cake's doneness (the forbidden-this-time toothpick and four others).
I find the springiness and sides-pulling-away-from-pan good ones in practice.
The internal temp is also reliable, but probably forbidden as too similar to sticking a toothpick in.