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Sounds like the input impedance on the speedo is a little high, great for isolation, bad for noise rejection.
Shielded lines to the sensors would help, auto electrical systems are inherently noisy especially as the battery ages. About the only way to clean this stuff off is to have decoupling caps hung off everything especially inductive loads. The ignition coil and alternator windings generate most of it.
Hang a capacitor off the positive side of the coil to ground and this will probably clear up. The ignition coil is the worst source as it's got a long path through small gauge wire to the main filter, the car battery.
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