simple periodically switching circuit
If you are making a lot of them, a small microcontroller with an internal calibrated RC clock (typically good to about +/-1%) will be the lowest cost solution, well under a dollar in smallish quantities. You would need a toolchain that supports the micro (software) including a cross assembler (or compiler) and a programmer or programmer/debugger (hardware). You can get the former for free and the latter can be less than $20 so it's not necessarily going to break the bank. The PIC12F1501 is one such part, available in an 8-pin DIP or smaller packages. However it's a little lower than I'd recommend in general because they left out the debugging hardware and you therefore have to use a header board for debugging, which isn't as convenient as a slightly more capable chip. Of course if you're making lots of them, unit cost is the important factor so I do specify them. 

However, if you're happy with the Arduino, and just want it a bit smaller or cheaper you can get a clone nano board for $2 or so and it has very little extra on there- a serial chip, a resonator for more like +/-0.5% accuracy etc. Since the serial/USB chip is on there you don't need the programmer/debugger hardware. It is smaller in footprint than a 40-pin DIP IC. 



Note that in either case, the clock accuracy is such that it might drift by many minutes every day (cumulative) - 1% of 24 hours is about 15 minutes- so if you start it out pulsing at night, it won't stay that way. These days if you really need it to work at the same time each day it might be easiest to go up in complexity (greatly) and have the device use an internet connection to set its internal time.