Sorry, poor phrasing on my part. The first two sentences should have just been combined to say you need to find out who owns it before the question can be answered, which you already know.
A lot of the topo / trail map books for a state will show the BLM land in a certain shade. You could try one of them first, and they're really handy anyway if you don't already have one.
There might be some rules about being on the side of the highway though, or even if their isn't the local LEO might suggest a different spot. ... actually, the local sheriff might just happen to know who's land it is if you ask.
If it's not BLM land, you might look for a ranch house somewhere in the area and just drive up and ask if they own it or know who does.
Short of that, you might have to go to the county courthouse and ask where the records are for tracts of land like that. GPS coordinates aren't a bad suggestion, but depending on the records it might be easier to reference "land west of mile marker 147 on hwy 17". The court clerk might be able to help there too.
The good news is, if you can find out who owns it they're almost guaranteed to say yes if you offer to help them with their rodent problem.
Heh, hopefully someone else will have some better land research suggestions for you