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Sure, a typical way is to use a cookie-based touch persistence library like Conversion Path.
Note if the form is literally on the *next* page view, you can Autofill hidden fields from Referrer Params (= query params on the Referrer URL). No need for cookies in that case.
I figured using cookies would be the ideal way to collect this info. Thanks for the tip on the referrer param, that's a start at least to collect some data in the meantime.