You don't need to remove the switches to test their function. With the breaker in the off position and no power going to the stove/oven, remove the conductor that connects to the lower right terminal of the suspect switch as shown on the schematic (it provides power to the indicator lamp) along with the switch's center terminal L1 conductors, there are 2 shown, perhaps grouped in one connector. Once removed, with the switch in the "on" position and your multimeter in Ohms and squeal, touch the two terminals on the switch with the meter's leads and record the numbers and if the meter squeals. It should display both.
Now turn the switch to "off", if you get anything other than "OL" on the meter, (which means open leads,) or hear any stuck pig, the switch is bad. A good switch will display neither numbers nor noise.
If the latter is the case, it could have been a wiring terminal inadvertently making a connection to the L1 terminal on the outside of the switch that illuminated the lamp. Clean everything up using acetone or equal & a small stiff brush, then put it all back together as you found it, making all of the connections clean and tight and ensure that they are not touching each other. It might work just fine once cleaned and reconnected.
If the switch is truly bad you need to rebuild it or replace it.
Good luck with whatever you chose.