Circuit broken alarm light
Instead providing you with a circuit I would like to propose an alternative solution.

Did you know that if you run a light bulb at a lower voltage it will last a lot longer. What I propose is to connect two identical light bulbs in series.
If you are currently using a 40 W bulb and you connect 2 in series they will burn less power so maybe you will need to increase the wattage of the bulbs, for example 2 x 100 W in series to replace the single 40 W.

This way the light bulbs will run at half their nominal voltage and their lifetime will be much longer than the nominal 1000 hours. The relation voltage vs lifetime is very non-linear so my guess is that at half the voltage the bulbs might last more than 10 times longer !