You DO NOT need to worry about the time spent while the phone is ringing; your message will be delivered when answered. But you do need to "wait" if the menu is not ready to have buttons pushed and/or a machine is speaking. You also need to know the necessary "button-presses" needed to get to a human or voice-mail box (do some recon). Multiple phone menus can be navigated. Here are some examples:
Call is answered. Robot waits 3 seconds (6 x "w") while the menu is speaking/listing options. Buttons 1234 are pressed. Robot waits 2 seconds (4 x "w") to pause over a possible "please wait while we transfer your call" message. Your bot-message is then delivered to a person or voicemail.
Call is answered. Robot waits 6 seconds (12 x "w") to pause over a mobile or landline voicemail-greeting. Your bot-message is left as a voicemail.
This navigates through multiple menus before delivering your bot-message to person or voicemail.
This waits through lengthy pre-recorded voice-greeting, enters 0 followed by * to get to an operator, then delivers your bot-message.