In general,
(1) If the compound has NO solubility, then the (non-ionized) ionic molecule is NEUTRAL in suspension and suspended particles will not move in the applied electric field,
(2) Any colored (ionic) compound that has slight solubility will give a colored solution, and the ion with the chromophore will move in the field. Search the on-line Sigma-Aldrich catalog for any of the hundreds of available dyes (acid blue/black/orange/ red/yellow etc or basic green/blue ..etc). For the undissolved solids, see above.
(3) Select e.g., any dilute acid as the colorless conductor.