Wow I just had a faint memory of this the other week! In particular, one of the stamps is a rabbit that I had the faintest memory of. Just did some digging and turns out it was from here: http://www.gemtree.com/
I registered and currently manage one of these .gov domains. Registration took some time, but it was an interesting process and felt pretty cool once it was finally provisioned!
I have a vague recollection of a piece of software distributed by Bank of America in the mid-to-late 90s that featured an interface similar to Microsoft Bob. From what I remember, it was similar to Quicken. Was never able to find any information about it, and granted I was probably 5 when I found it on the family PC so the memory is a little fuzzy, but seeing these old design languages from that era of computing is always neat.
I think you're right, although I've noticed that there's a timeout where newer cars automatically turns off if the key fob doesn't come back within range after so many minutes. Probably a safety feature to avoid accidental walkaways, whereas the button required a deliberate two-step action (hold down while turning and removing the key) to activate the feature.
At first glance this reminded me of some Ford Crown Victoria Police Interceptor models which had similar unlabeled buttons. One would disable all exterior lights, including brake lights, for going into stealth/surveillance mode. An adjacent button was used to be able to remove the key and keep the engine running, while preventing the car from being shifted out of park until the key was inserted again. I haven't seen either feature re-introduced in the newer Explorers or Fusions though.