The burrow could be in your neighbor's yard. Anywhere you see loose dirt and a small hole.I have no idea. So far I've seen the one, identified by the pattern on its tail. The issue at least starting to eliminate them. I can't have the chickens in the run with active traps and the stupid rat only comes by during the day so I can't try and trap them at night.
The only idea I have is to double up the trap - get a small Have-A-Heart cage trap (I saw an idea for an upside-down milk crate which looks like it would work) and put the actual rat-killing trap inside it. You could even cover the cage sides (or all of the milk crate holes except one, and place the killing trap far from it), to keep any nosy beaks away. Or cover it all and make a long tunnel to the entranceway (we do this for woodchucks when they start bothering our plants). The cage trap would have to be tall enough to accommodate the action of the rat-killing trap. This cage is either 4.5" or 5" tall:
https://www.walmart.com/ip/Mavis-La...mC_AmHlnyj1LtcoNqMsJmRTZO79P5QhkaAvixEALw_wcB