If you use another relay that can switch between inputs then they will be separated and the output will be either from input one or input two with no interference.
However you would get a break in operation in changing from input one to input two.
I am sure there is a better way of doing but cannot remember how at the moment.
I am also not sure of the power requirements you need to operate an engine ignition switch.
In this diagram input two will override input one.
I am not familiar with American cars. But the lads are right , more info is needed .
If these are ECU controlled electrics the Engine control unit. may be reading the extraneous current and shutting that circuit out .
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