Ambō is sometimes decline to match its respective noun, like a fully-functional adjective, but otherwise remains fixed as ambō
- Ambās mānūs lavit: he washed both hands.
- Consulēs alter ambōve prōgredientur: either one or both of the consuls will march on
- ūna salus ambobus erit: both were healthy (this is Virgil—a very Greek declension!)
Effectively, there is no rule. Both A&G and L&S present freeform variation between the two options.