Last winter we arrived in February and had no problem finding a lot in the Fortuna Foothills. As previously suggested, just drive around. For rent signs are often posted on the lot. As I recall, we payed about 300 bucks per month including water, sewer, and electricity.
the Yuma White (and Green) papers often have rental ads, as does Craig's List.
Schechert Estates is the farthest out, in the southeast corner. A good plan might be to start there and make some sort of search plan and drive back and forth over tge quadrant, though gas consumed isn't a trivial factor these days. But grab a temporary site at a park (might be worth reserving in one fir a few days at the beginning).
There is also a North Foothills, which is north of I-8. I don't know anything about it, but I think it is probably more oriented toward permanent residents.