The 1997 Neon uses a vehicle speed sensor (VSS) for speedometer function, and it plugs into the transaxle’s extension housing. It is gear-driven off the output shaft, sending an electrical signal to the PCM and ultimately, the speedo head. Having the VSS output checked would be your next step, as well as inspecting the small gear that is attached to it, which may be loose or have stripped teeth, causing erratic signals.
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It sounds as though you may still have a bad connection somewhere, or the speed sensor might be bad.
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