Scott and Albert: I have removed the K600 relay tube (6NO45T marking on the chassis ... no clear/visible marking on the tube). I applied 6VDC to pins 1 and 6 and although the tube is warm, the N.O. contacts did not close even within 90 seconds (2x the spec delay). I did this test directly on the removed tube rather than hunt down the tube socket connections just because testing the tube out of circuit was easy. So I suppose this confirms the time delay relay is an issue and no need to get to board level tests.
I do like the idea of modern replacement. Used tubes on ebay look like $10 or more.
Thanks.