I am very sorry about your missing cat.
My cats all have a good home, love, good food and kitty companionship and still they have all gotten out.
I think most neutered and spayed cats go missing because they get curious. She may have been going on little adventures before but the terrain was much more familiar. My bet is that she went too far and got lost. She doesn't have the usual markers to help her find her way home.
Most of the time the cats are near. A timid cat will hide even more. What I suggest is for you to put some of her toys and things outside so she will recognize the smell. I even sprinkled some soiled litter in the yard. She will be familiar with Elijah's smell. If Elijah is talkative open a screened window so that she can hear him meow. Get a flashlight and look underneath things. I found mine underneath houses. The best time to look is nighttime because she most likely will feel safer then. None of my cats came when called because they were frightened out of their minds.
Becky disappearing is no reflection on you or how happy she is at home. They just get nosy and sometimes it gets the best of them and they get lost.
Sometimes they may try to go back to the old house if it close enough.
Good luck and some vibes for Becky's safe return.

