In your example "тоже" will do too.

Your rule is good as a first approach. But I think in most cases "тоже" can be replaced by "также" but not vice versa.

Также sounds more official than тоже so if you want to turn a text into officialese replace all "тоже" by "также". But for a good literary text "тоже" is better. In my opinion overuse of "также" is just disgusting.