Can the Tenseigan reactive and deactivate like the Sharingan and about the Rinnegan why was Nagato never able to deactivate it but Madara was able too.
The Rinnegan never belonged to Nagato in the first place so he can't deactivate it. Madara was the original user so he could deactivate it when he desired. So much about the Tenseigan hasn'tt been explained since it only came in a cannon movie but I think once you awaken the Tenseigan it can't deactivate back into a Byakugan but it does have Hamura's chakra plus the Byakugan abilities.
Its like Kakashi having the Sharingan. Since he isn't an Uchiha its always active so he covers it so that he isn't actively using it. If he didn't it would consume too much chakra.