Hello Samantha,
From the description it is the Carver Caravelle SBE 1800. - all controlled from the wall switch.
Normally, If the gas flame is not igniting, the controller should try two or possibly three times before locking out. This is displayed by the flashing green light which is what your previous one did.
For some reason your controller is not locking out properly, thus the controller or the flame detection electrode in the heater is faulty .
The heater must be quite old, so I have to ask when it was last fully serviced and cleaned out. This will establish what is at fault.
Because it is a gas appliance all installation , service, repairs or removals must be carried out by a competent person.
Gary from Arc systems often contributes to this forum , and he does carry some spares for older Carver models. Perhaps he might be able to help with a replacement controller.