That's the wrong way to go about it. Your engine starting battery is absolutely sacred - never "steal from it" for appliance power. In other words, don't be Jesse in Breaking Bad ("Four Days Out", Season 2 Episode 9).
Lead-acid is for starting engines, NOT boondocking
Lead-acid has a very short life as batteries go. It is bad at deep cycling (which is what you need for boondocking). But it's good at starting engines.
In the 1890s when electric cars were more popular than gas, the "nickel-iron" battery was preferred, and lead-acid was considered trash. However when the "electric starter" was invented, that was a game changer for gas engines. But it depended on the one thing lead-acid did better, which is provide a huge WHOMP of energy to stat an engine. Starting engines is the "killer app" for lead-acid batteries. A match made in heaven.
This match took over the world and dominated for 100 years. And here we are today.
Now if you design a lead-acid battery from the ground up for deep-cycling (like an electric golf cart), if you want that battery to last, you can only use about 30% of its cycle everyday. So if it holds 1000 Wh, you can use 300 Wh everyday. If you push it harder than that, you will shorten its life and shrink its capacity everytime you do it. So a lead-acid battery is a lousy choice for deep cycling generally.
However, your car's starting battery is NOT optimized for deep-cycling. It is optimized for starting. If you try to deep-cycle it, even 30%, you will rapidly degrade the battery and then you'll be stuck like Walt & Jesse. So don't do that, don't even think about it.
They do make "Starting+deep-cycle hybrids" but even then, you don't dare use more than 30% of capacity regularly or you'll degrade them. 300-400 watt-hours doesn't seem like much to me. 300 watts of solar panel (which isn't much of a panel) would fill that in an hour. Then what?
Your best bet is batteries specifically for deep cycling.
Even "specifically for Deep-Cycle lead-acid" batteries kind of suck at that. And, car wrecks are causing a glut on the market of "lightly used" electric car batteries to be available. As such, the thrifty boondocker has a huge opportunity to "do it with lithium" and actually save money for the same usable watt-hours.
Mind you, learning the tech and using a Battery Management System is non-optional unless you like RV fires.
Could we just have one "master battery" and dump the lead-acid starting battery? Maybe, but the lithium pack would have to be huge, like 10KWH - we're talking a whole Tesla PowerWall. That's not a technology limit, pro battery manufacturers can do it - it's a limit to DIY abilities using former EV packs that aren't made for such surge currents.
Lead-acid batteries are cheap, just dedicate one to engine starting IMO.
Now, used lithium batteries on eBay run about 20 cents a watt-hour and you'll need a BMS, bus bars and other kit. That seems like a lot compared to lead-acid at 10 cents a watt-hour, but 80% of the lithium's range is usable without damage, whereas only 30% on a lead-acid.
Obviously, put the lithium pack not under the engine hood because they don't like heat.
To answer your question, though
Yes, low voltage cut-offs are readily available for the purpose you intend, marine and RV shops should sell them. However their default setting may be much too low, and would allow you to dip the battery down 60-80% (which would age it rather rapidly). I would set it more conservatively.
Honestly 300WH isn't much and I would be looking at options for a bigger pack. Lithium is a great way to go if BMS and balancing is installed.