I need a solution to use one momentary switch to switch between modes on a pump. Off (NC) | Low | High. What I mean is you push the pushbutton once to turns pump on low, push it again for high and again for off (NC). Additionally on low I'd really like the switch light to flash slow, and on high the switch light to flash fast. I've seen it done with Raspberry pi (https://www.youtube.com/watch?v=LOwnG5Vhzcs) but would like a simpler (maybe relay) option.
No need for a MCU even, simple 74HC logic would work just fine.
- De-bounce the switch with RC filter. Normally open, ie press switch=voltage comes through.
- Give it as input to a decade counter IC like 74HC4017. Ouput pin 0=off, 1=low, 2=high, 3= wire to chip select of the IC, use a BJT or similar to inverse polarity of the signal.
- Add some driver IC or MOSFET to the outputs, then let these drive 5V coil relays. Flyback diode across the coil.
- Decoupling caps and TVS on the usual appropriate places.
- For blinking lights you can use LEDs with built-in flashing logic. Supply these from the relay outputs.
Your did not really explain what you want to do, but based on title (switching between three devices), perhaps simpler solution without complete DIY circuit might be to use ready-made microcontroller device such as Shelly or Sonoff. I know for fact that Shelly can be configured to control two devices with one momentary switch. This assumes that you control your motor speed with two separate On/Off switches and not via PWM or any other type of regulation.
As for light, it is really not clear what you want, however shelly again can trigger web request when something happens (e.g. switch is pressed), you could use it to change the light (via other shelly, or even simpler controller).
These days, the simplest solution to almost any non-trivial logic control problem is a small microcontroller. For a one-off prototype, look at something off-the-shelf, such an Arduino. For mass production there are many tiny little microcontrollers available at low cost.
Anything electro-mechanical with relays, solenoids and switches is going to end up bigger and more expensive.
Here's one, using two magnetic latch relays K1 & K2, three momentary push button switches S1, S2 & S3 and a diode matrix.
Freewheeling diodes and LEDs are not shown.
Using two LEDs to indicate 'Low' and 'High', instead of a single LED blinking at two frequencies, would keep the circuit quite simple.