If you have the switches connected properly, they are in SERIES with the battery pack and EI unit. The manual switch opens or closes a connection on one of the wires. The radio-operated switch will open or close a connection on the SAME WIRE. If you can turn one switch on and off without affecting the ignition of the engine, then the switches are wired incorretly.

For engines with the magneto, you have only one wire that connects the ignition unit to ground. You would put your two switches in that wire, again in series.