Gobby:
What you say you have isn't precise enough for us to say anything.
Many linear actuators use DC (Direct current as would be provided from a battery)
A "tranformer" only changes an AC voltage to an AC voltage.
Sp, you could have a 12 VAC synchonous AC motor with or without limit switches.
You could also be saying that your definition of a "transformer" provides DC, We would say a "120 VAC to 12 VDC power supply.
Mike asked the questions. This is very similar to a "chicken coop door". Egg turning comes up occasionally, Chicken coop come up more often.
If it already has limit switches, the process is easier. If the current demands are small, that can make things easier as well.
The general idea is to have two SPDT relays labeled OPEN or CLOSED or Position A and Position B. The limit switches are arranged to turn off the coil of the respective relay at a limit. The way the relays get arranged is that if both coils are activated or deactivated, the motor is stopped. The limit switches and the OPEN/CLOSE relays would use the 12 VDC power.
BOSCH automotive relays are cheap and designed for this.
A 120 VAC relay would connect to your time and alternate the OPEN/CLOSE signals.