The computer is powered by the ignition switch closing a contact that sends power to the EEC power relay. The power relay closes, and conducts power to multiple points on the EEC connector(s). If you have power all the time, likely causes are the switch, as noted above, and the relay. Sometimes the contact points on a relay wear, and can fuse together or get hung up such that contact is kept after the control winding is de-powered. The relay contacts should pop open, but may stick. If you pull the relay connector, either in the box, or a separate relay on the firewall/inner fender, the EEC should lose power and go to sleep. It does have power internally(KAM or external battery) so it can remember some settings on mixture and idle control. Later models have internal power, I think(may not...), while earlier have another external power source to keep the memory, labeled KAM - Keep Alive Memory for some reason.
tom