For authentication you have supplicant, authenticator and an authentication server. The supplicant is the user and their PC tablet etc, the authenticator is the Firewall and the Authentication server is the TACAC's server.
TACACS protocol is used to pass information between the Authenticator and the Authenication Server. The interaction between the supplicant and the authenticator will be something else. It could be web based auth where the firewall presents a login server, or some method of providing credentials via http, whatever. You most likley need your linux client to emulate the supplicant->authenticator mechanism, not TACACS.