Hard to diagnose without seeing it. As Sqzbox stated above, if it has a Full Manual Valvebody it will only shift by moving the shifter handle and wont have a Detent cable. Others will retain Automatic & Manual shifts.
Since you said it would downshift when you gave it more than 1/2 throttle it must have a Detent cable.
There are also Trans that have air or electric shift solenoids that are activated with RPM switches.