Reciever transmitter

"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 become active.

-- Sue

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.