[strictlypersonl]

It's been a few decades (OK - almost a half-century) since I took circuit theory, but I suspect that a large capacitor would dampen the sender's signal. Connect it from the sender signal circuit to ground to even-out the current going through the sender windings. Maybe someone with more expertise than me can give you a proper value. (For reference, the gauge compatible with the 33-270 ohm sender has about 100 base ohm internal resistance.)