Very Easy…
No doubt there will be suggestions to use a Arduino, RPi PICO or similar microcomputer. Persoally I find this overkill and unless care is taken accuracy can suffer (at least not meet my timenut leves) A lot of the low cost boards don’t even have crystal oscillators.
…
Robert.
Well, here’s an Arduino solution, more or less complete, that can be built at home. It’s not a list of suggestions requiring electronic skills.
The circuit:

Arduino Leonardo recommended because it has a crystal oscillator. About 100ppm, similar to a good mechanical watch. Easiest way to power it is with a 5V USB wall-wart plug.
I’ve used a relay module, described here, because it handles the volts, and isolates the Arduino from any spikes caused by the Pragotron’s solenoid. Very simple.
The program is also simple. Given the required frequency in hertz, this online calculator outputs a complete ‘blink’ program. It flashes the onboard LED and pin 13. The hardware timer in a Leonardo goes down to about 4 seconds, so I asked for one, and will show how to make the required 60s from that. This is the 1 second program:

To get 60 second pulses, modify the ISR code at the end to this:

No need to install the Arduino IDE or to learn C, or write a program.. The code can be compiled online and blown onto the Leonardo from here. A free account is needed.
There are some gotchas:
- where the 24V comes from (Maybe a battery – depends on how much current the solenoid draws and for how long.)
- Alan doesn’t specify what he means by ‘precise’. If better than 100ppm is needed, I’d add a RTC module (about 20ppm) , and use it’s seconds pulses. The program is different – let me know if needed.
- I’ve assumed the 60 second pulses can be a square wave, with 50% duty cycle. That’s heavy handed, and maybe something like ON for 0.1S, and OFF for 59.9S is wanted – it depends on how the solenoid ticks the Pragotron. If the duty cycle needs to be changed, it’s done by tweaking the program, no hardware change required.
Taken me much longer to document than to do!
Dave