"Wireless door-bell" springs to mind as the data communications method.
Some come with battery receivers that aren't much larger than a key fob
and can be re-engineered to be much smaller, if the endurance required
allows for a smaller battery.
Pressure sensitive mats come in switched output form - so easy enough to
wire across the bell push button contacts. If they are the changing
resistance type, a simple comparator will do the job.
Movement detection is a bit trickier. You could use a PIR sensor that
provides an output signal that is used as the source for the mat. Thus
the PIR would have to be detecting movement *and* the pressure mat would
have to detect pressure, in order for the input to the transmitter to
so is this key fob the transmitter?
and you want a closure when a pressure mat is activated after a time delay?
probably a simple R-C (resistor - capacitor) circuit, depending on how long
a delay you want, should work.
You may have to us a transistor or something to activate the transmitter.
Just hard wire to the transmitter and you should be good to go.
Here is a handy calculator for R-C time constants.
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