Does dead mean 2vdc, 5vdc, 11vdc ? The Fuso battery requirements call for 950cca which is pretty generous rating.
The past few years the smaller, handheld power packs utilize super capacitors. This design uses residual voltage from the battery to charge and amplify the capacitor ...similar to portable heart defibrillator...and releasing the energy in hopes it will have sufficient boost to start the engine. This design is smaller and lighter than the previous booster packs using legacy motorcycle lead acid/AGM battery (heavier and larger)
The larger the capacitor rating, the better your chances of being able to start the vehicle. But larger capacitors also mean a larger booster footprint which isn't always consumer friendly. As an aside, the capacitor isn't designed for long, drawn out cranking.
blah blah....to answer your question, a separate car battery would be good but the drawback would be 50lbs or more. a large motorcycle size lithium battery could be considered and weigh less than 10#. A good companion for the lithium cell would be one of those ubiquitous handheld booster/jump packs with the largest capacitor you can handle. If the handheld booster pack isn't able to start the Fuso, it can be 'recharged' using the lithium cell. Additionally, if your overland equipment already includes a large Jackery type pack, that could be used as a 12v power source for your jump start but I've not tried this first hand yet.
I'm actually bench testing (not yet field testing) super capacitors bundled to the size of a 6-pack of beer since I had the same thoughts and questions you posted