I haven't used the venerable old NE555 for about 30 years, because it is so noisy it disrupts the supply voltage levels if there is any sort of load on it at all. It's also pretty noisy if the frequency is low, since the timing components then, if not well chosen, draw lots of current. These were sometimes handy to generate the +26 volts used to program EPROMS back in the day ... but those days are gone and there are CMOS devices that are MUCH less noisy and MUCH more stabile.

My suggestion was to derive the desired clock frequency by dividing it from the "X2" (Pin 18 of a DIP-40) oscillator output thereby producing a clock totally synchronized, hence not slipping back and forth around the sample strobe (inernal to the MCU) that samples the external signal input. If she's unwilling to do that, well... she's on her own, as that's a solid and basic way to ensure that the firmware works as necessary. She can deal with the vagaries of the NE555 on her own later, trying precise timing cap's and 0.1% resistors, if she wants.

Anyone who uses that old '555 when he/she could use something less troublesome, e.g. a CMOS schmidt trigger with a single feedback resistor and small capacitive load, gets what he/she deserves.

The principal benefit of using a digital divider as previously suggested, referenced to the MCU oscillator, is that it will be exactly synchronized with the MCU. That will allow precise verification of the code. If the reference frequency varies, introducing inaccuracy, the divider will track it, thereby nullifying the inaccuracy. This is something that can be done without any scarce or possibly unavailable resources, e.g. frequency counter, oscilloscope, etc, which is, in fact the reason I recommended it in the first place, since the design of a divider from 12 (or 24) MHz to very nearly 780 Hz is very easy to design and construct.

RE