If you look at the pic, I plugged a spade male into one of the output lines there below the relays that is hot when the car is running. That output triggers the relay to latch. You will need some kind of relay to disconnect the two batteries from each other, or you may be stuck with two flat batteries and not be able to start. I saw the reviews, but frankly, have no idea of what they are talking about. I have had it in there for over a year without issues. I did check it once with my IR thermometer to see if it was an issue and it is frankly cooler than the other relays installed by LR there in the power distribution spot.
Note on Amazon reviews. If you note, this relay is a great example, it is sold by a plethora of different vendors with different labels on the same relay. I think they talk trash about each other and the negative ones provide little details of why. Relays have a coil, this holds the contacts to together. If it is a poorly insulated coil it may get hot. The biggest reason it may get hot is if somebody tries to hook in a fairly large battery that is flat. It will draw, most likely, more current than the contacts are rated for. Then it will melt. You need to ensure that your batteries, in a simple system like this, are AGM lead acid. If you try to mix battery types you can run into problems as they require different charging rules than lead acid. Most of the overpriced charging panels folks seem to flock to are actually just a smallish relay hidden behind cool looking LCDs. A relay is pretty much a relay. You can get a super beefy one, like we use on aircraft, but then, expect to pay hundreds for just the relay. With smaller batteries, like the one I am using, do not draw more than 10-12 amps on initial charge. If they did, I would be more worried about the wire size than the relay. If you downsize the wire too much, then it acts like a resistor and gets hot on its own. All this needs to match up electrically and load wise. Batteries can draw a surprisingly large inrush current. On my Twin Otter aircraft, its starting battery pulls 3,500 amps on initial inrush after a start. That is enough to actually weld with, but it only does that for seconds. The contactors have double ½" contacts to handle it and the wire gauge is huge. Electrical rules and current heating rules are fairly simple, too much current = heat if the pipe it is trying to pass though (relay or wire) is too small.
Be reasonable on what you want to have invested in in car batteries. Remember, too much weight makes you car handle like crap and get poor milage. Batteries are literally lead. Now I was given as a gift, one of the power lunchboxes, or actually cooler sized. It is lighter weight, seems to last a reasonable amount of time has all kinds of outputs, USB A through C, wireless charging on top and an inverter along with 12V. It just takes a fairly long time to charge, especially on solar or 12V. Amp for amp output it is far lighter, just expect it to be charging all day. I do not think I would mount LiPo batteries permanently in the car. A small deficiency in your charging setup or an external factor may cause your vehicle to light off. The tech is evolving. I kept it simple and low tech, I must have almost $50 invested in the system. It works, trouble free. I am moving on to the Defender now, which finally made it to the dealer after a six month order wait. Of course it is waiting for a magic cable that seems to be defective on arrival.