The problem is that I find it very hard to find these businesses, and indeed most of them don't actually have enough work to fill more than a couple of days so you would need a reliable source of these gigs if you want to survive (you can't charge insane amounts to compensate either as these businesses just can't afford it).

You should work for a system integrator if you want to do that kind of work with regularity. The integrator contracts you out to those companies as needed, and you develop a niche and maybe customers start asking for you by name. In the best cases the integrator is your employer and offers full benefits, as well as absorbing the costs of downtime.

That business model can also be abusive for obvious reasons. I can recommend a good company if you're interested.