Detecting the amplified signal won't work. There are these things known as directional antennas...
The timer idea is a good one, although a ns-accurate timer is starting to get a bit much for something to put into a key fob. Especially give it's run off of a watch battery (power requirements) and often exposed to heat / cold (thermal drift).
The timer idea is a good one, although a ns-accurate timer is starting to get a bit much for something to put into a key fob. Especially give it's run off of a watch battery (power requirements) and often exposed to heat / cold (thermal drift).