GPT looks valid. Diskutil sees empty disk
The problem turned out to be the PMBR.  My first attempt was to copy sector 0 off a GPT formatted memory stick.  

Examined that with fdisk and it had partition of type EE, but start and end cylinders were the same.

I edited partition 1 and accepted defaults.

fdisk on mac will report "can't get exclusive access to write sector back, reboot required"  It lies.  You don't have to reboot. 

After doing this diskutil was able to see both partitions.

I was unable to repair the first partition, used for time machine, and ended up reformatting it. (Even after it was a recognizable partition, diskutil would start on it, and give up in a few seconds.)  (I didn't try very hard.  The really important stuff is stored on drop box, on a mirrored disk on another machine.)

@Klanomath deserves credit for GPT disk.  I had found this, but missed the fact that it provided Mac binaries.  I'm not used to binaries on Source forge.  GPT disk appears to be a useful tool for dealing with this sort of situation. It would have been a better way to go.