Hi missouri massey man,
I went there this afternoon and confirmed that it was a standing pilot. The renter had used the correct procedure to try to relight the pilot (except that she used a match, and it turned out that it did have a striker type ignition button). I couldn't make it stay lit, either. I removed the thermocouple and cleaned it, and cleaned the pilot assembly with a soft toothbrush. N/G. I brought the thermocouple home with me, and I'll replace it tomorrow.
You mentioned that I'd need several wrenches and a long phillips. Is the long phillips to remove the whole pilot assembly, including the thermocouple? That assembly was mounted to a fixed tab with two phillips screws. I couldn't get enough purchase on any screwdriver to loosen the screws, but that was partly because I was handicapped by not being sure that that was what I wanted to do. If I know that I can safely remove the whole pilot assembly, I'll figure out some way to get the screws loose. But maybe there's no benefit? I should be able to replace the thermocouple just as it is---I took the existing one off and put it back on once already. I wouldn't take the pilot assembly off unless there was reason to believe that it was part of the problem. What do you recommend?