In preparation for providing a drawing, I stripped off the board the battery holder, socket, and crystal from the standalone 1307 I tried earlier (they were not wired, but were cluttering the board), then began commenting out the unneeded code to post the minimal circuitry and programming that demonstrated the problem. Somewhere along the way... it works as intended now.

You may recall that the last thread on this issue ended with my determination that it was some undiagnosed power issue related to backup battery voltage; I was not able to isolate the issue. Once again this is the case.

I am tempted to write it off as a bad soldier joint or poor connection; it hurts my pride to admit such - I was a hearing aid technician for 20 years and close tolerance work was my bread and butter; yet, I cannot think of any other cause or issue that might manifest itself in so frustrating a way.

I am looking now for a new DSO and I am convinced to get one with a logic analyzer. Issues like this are so demotivating...

Thank you all for your suggestions and your effort and advice, I appreciate it very much.