When I toggle a push button switch on and off, instead of getting a pure on/off continuity levels I sometimes get "transitional" values. I need it to be purely on/off with nothing in between. What components do I need to add to the switch to make that happen?

One thing you could try is a relay. It is a type of electronic switch.

Look up DEBOUNCE circuity. All mechanical switches "bounce" a certain amount. Including Mechanical relays. There are ways to minimise its impact electronically.

Try a Solid State Relay
https://www.omega.com/googlebase/product.html?pn=SSRL240DC10&gclid=EAIaIQobChMIr6Pg36O11gIVhbbACh34KwpAEAQYAiAB EgJl0_D_BwE
Check Specs and Prices, Above is am Example, They work well.