I've always kept mice out of most EVERYTHING by plugging holes with steel wool; it might work well with those openings in the battery box provided you keep the steel wool away from the connections.
'16 JAYCO 154BH SLX, Baja Ed
'13 Silverado 1500LT, 4WD, Ext. Cab, 5.3 ltr.
"Fair Winds and Following Seas"