Ah ha.

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I remember, now, why the toilet would be blocked.  The day I was leaving I was dumping wash water from a tub.  I thought it to be empty.  It was, all save a spoon.  And that spoon shot right into the trap, beyond sight.  It was a big spoon, tablespoon sized, plus.  Solid metal, a bit oversized even for it's intended uses.  So... that is what the problem is.  Before I remembered I tried the snake.  Now, the snake does open a channel which allows enough flow to vacate the stool but it doesn't seem able to catch the spoon and bring it back.  I'll keep tinkering... if I can stop needing to use the facilities.  Oh, I'll... get it sorted before long.  At least I can use the toilet, in a bit of a limited capacity.  And now that I know what the problem is I might be able to figure out a better solution.  I am wondering about fishing hooks, though...  I'm just not sure.  A spoon is going to be a little tricky, especially being as heavy as it is and with a trap that allows it to simply slide out of sight.  Looking at the trap, patterned into the ceramic, it doesn't seem like it should even be able to do that.  So much for looks.

I really thought the plumber snake would catch, or would sort of get tangled on it, and pull.  But nope.  Oh well, live and learn.  At least I don't have a wife and a dozen kids wanting in there.  Now if I could just tame my own needs.  Something about getting home...  Do we have to mark our territories, even if we don't think of it that way?  Don't know.  It is definitely incentive to get going on my en suite bathroom.  Two of everything, even in a home, really eases maintenance and other problems.

Later.