Depending on the year, make, model and engine there may be one or two solenoids and there may be other relays involved in the starting process (Will do the "other relays" later)
For example.. On a car my daughter once owned there was a recall.. Seems the starter solenoid pulled enough current to set the ignition switch on fire. So they put in what is called a "Pilot Relay" (A smaller relay that keys a much larger relay (Solenoid) that causes something to work) Some vehicles are designed that way from the drawing board.
It may be the pilot relay you are hearing, but if it's not making contact.
Page 2.
The "other" Epically in a motor home you might have relays for several devices on the ACCESSORY board, and there may even be an automatic "Disconnect" Solenoid all of which click when you start the ride.
That said: Knowing how to "Work around" a failure.. VERY IMPORTANT, and it appears.. You know.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times