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It won’t be possible using GEO Job Manager. GEO Job Manager hooks into WP Job Manager by adding its own fields to the form as well it modifies the search query.
In order to do what you want you will need to modify WP Job Manager plugin. And still I am not sure it will be possible to have the search form in one page and the results in another page without “heavy” modifications.
Anyway, you will need to contact Mike, the developer of WP Job manager and advice with him.
You could do it ( build your own custom search form and custom results page ) using GEO my WP plugin.