I watched the first 2mins before I got annoyed..
As I said, the starter motor system has been beefed up to take account of the workload it has. John T's 30 year old car will be very different.
He is right that it doesn't actually save much fuel, a lot of the benefit is reduced emissions in built up areas.
The first diesel with stop start I drove was horrendous, they are much better now.
The real benefit comes with mild hybrids where the engine cuts out below 20kph say, and regens on the braking. This can bring appreciable economy benefits by avoiding the initial pull away on ICE. My previous car was a PHEV which took it one step further again. Averaged 42MPG (6.7l/100km) in a 280bhp 2.0 turbo petrol. Still averaged 38MPG with (expensive) electric costs included
re. the buttons a quick look on car sales pics shows a likely looking button in front of the gear lever, in the shadow next to the parallel park button?