Mechanical lamp timers I have seen may not have 15 minute switching increment. And, unless a mechanical lamp timer is on a UPS, the clock "falls behind" when there is an electric power failure. I have seen digital-based (instead of mechanical) lamp timers that have battery back-up for the clock and keep time accurately enough to comply with FCC transmission system operation rules. Key point is accuracy of the clock, and knowing exactly what will make it malfunction.
So far, I have not seen an inexpensive lamp timer that can be programmed for monthly switching. This might not be a "flaw" because it means someone will need to look at station technical operation at least once a month, and a little TLC goes a long way.
I recommend visiting the transmitter site(s) once a week, at minimum.
There are broadcast-oriented remote controls available at the approximate $600 price point. Someone could make a timer with a programmable logic controller, but at some point the value of the individuals time is worth considering.
My recommendation is read and interpret the FCC rules and put something in place that is compliant.