Here's an idea for under $20 that I am going try that I found on Amazon. It is a BN-LINK 7 Day Outdoor Heavy Duty Digital Programmable Timer that you can set up to 8 on/off programs for the timer’s two grounded outlets. Both outlets are controlled simultaneously, and settings can be as short as one minute. You could set it to turn on for a few hours one or two days a week to top off your batteries. I have already installed a small 2 amp trickle charger on the chassis battery that I also plug in with my coach batteries to a 115 volt 20 amp outdoor outlet. I have been doing that for a few hours once a week for now, but I'd like to "set it and forget it" this way. Charging my coach batteries usually draws only a few amps with nothing inside running so I'm sure it wouldn't overload the timer, which is rated at 15 amps. My coach is a 2005 Winnebago Adventurer 38R, so I want to minimize the time it is plugged in so I don't overcharge the coach batteries since it doesn't have a "smart" charger/converter. For your set-up, it would only annoy the rodents for a short time every few days, but that might be enough to keep them from moving in.
✓ VERSATILE & CUSTOMIZABLE: Easily set up to 8 on/off programs for the timer’s two grounded outlets. Outlets are controlled simultaneously, and settings can be as short as one minute.
✓ JUST SET & GO: Choose your own individual days or simply select one of the convenient pre-set combination days. Switch to Daylight Savings mode with a press of a button. Please Install one AA Battery(not include in package), the long-lasting backup battery keeps your settings even in the event of a power outage.
✓ PROTECT YOUR HOME: Activate the “Random” Vacation mode to randomize your programmed lights. Make your home look “lived in” even when you’re away.
✓ FOR OUTDOOR AND INDOOR USE: WEATHER PROOF construction for the outdoor Christmas/garden/landscape lights, pool pump, fountains and other electrical outlets.
✓ SAFE & RELIABLE: Heavy duty material, 18 inch cord, and two grounded outlet makes it safe and durable. Rating: 125V, 60 Hz, 15A/1875W Resistive, 8A/1000W Tungsten.