In the Civil War the when Cavalry would rout an Infantry’ it would then pursue the retreating Infantry. Borrowing a rule from MM44 (Armor Overrun) here is a suggestion for the Cavalry.
On a successful Close Assault Combat, an ordered Cavalry unit may move into the vacated hex and may then battle again. If the ground the Cavalry took during the battle puts you adjacent to an enemy unit, this second battle must once again be a Close Assault Combat. A unit may take Ground again after a successful second Retreat-Pursuit. However, a Cavalry unit may only make one Overrun Combat during a turn.
All Battles, Close Assault and Overrun Combats must be completed before the next unit may battle.