If you are careful , you unscrew the sw off and install the new one immediately [ without touching the pedal ].. but you do not tighten it. You then have someone press the pedal to get any residule air to come out the loosened threads..then tightem the sw. You are basically using the sw as a bleeder b/c if any air did enter , it would be right at that switch port and not into the sytem.. that way you do not have to push the air all the way thru to a bleeder. Check fluid level too.........
You may hust want to change the fluid while you are at it..a good maint. procedure that most who know brake systems do every 2 years.....

Did you try the blower test??

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A Dalton