I was told that here you don't have to close a flightplan, but I was worried that if you didn't, then SAR would be scrambled? I was told that this isn't the case.
If the flight plan is not closed in due time - i.e. after the "endurance time" you wrote - then they basically have to trigger SAR, yes. Over the years they have learned that people tend to forget, so before trigering such an expensive operation, with no certitude that you'll be able to pay for it, they'll go some length to make sure you didn't simply forget. Normally they will try to call your filed destination and alternates, and if you mentioned your mobile number in the flight plan they will call that too.
In many cases your flight plan will be closed for you, normally by the tower of the field where you land, but I am never sure if this is mandatory. It never hurts to ask, so as to be on the safe side! If in doubt, call one of the adressees on the phone after landing.
In all theory, closing a flight plan can only be done after landing. For non-radioed/non controlled fields, some countries allow closing through the FIS, when "destination field in sight" is reported.