Welcome from NJ,
The Run part of the switch tells the EHC to send power to the Ign control module and the Start button sends a signal to the EHC to activate the compression releases and the starter at the same time.
To bypass the on/off you would need to install a switch to send 12 volts to the Ign module. Also you would need the slam button that SCC007 suggested in order to crank your starter. Both are nice to have as a
back up if your EHC craps out. If needed, you would have to manually push in one of your compression releases unless you have extra hands available.
Unless your interested in the
Back up starting system it's would be much faster to just replace the Rt side switch.
This link will help you verify that the switch is indeed your issue. Cleaning the connection may be all you need. Good Luck