Power Inverter in Tool Box charging booster pack

I recently had a dead battery and decided I needed to invest in a booster pack. I foresee having a problem remembering to take out the pack to charge it every month or so, besides, I like tinkering with things. What I want to do is install a power inverter in my toolbox. I was thinking running some heavy wire (maybe 2 or 4 gauge) back to my toolbox from the battery and install a relay switch close to the battery that will close the circuit when the key is turned on. I have wanted to do this in the past to use small things like drills and saws while working on the farm. Every time I turn on my truck, the inverter will be working just to have the pack topped off to prevent the monthly charging and I think it may work to keep the battery in better shape for the booster pack as the pack I bought has an automatic charger that claims you can keep it plugged in indefinitely. When I use the booster pack and drain the battery significantly, I anticipate plugging it in at the house to do a full charge. My question is this: is it dumb to convert your 12 volt dc from your car battery to 120v to keep a 12 volt booster pack pack charged just in case the car battery ever has a problem? ... Or should I just set an alarm on my phone to remind me to charge the pack? Thoughts?