The intermittent character of the problem makes it difficult to trace down. I had been thinking about using a remote start switch to bypass the key switch for diagnostic purposes.
Let me see if I have Barry's suggestion correct:
The heavy starter cable comes from the battery to the back of the solenoid. There is another cable going from the back of the solenoid down to the starter motor. I need to put a test light on this 'output' cable and monitor the current when I use the remote start switch. If when it 'clicks' and doesn't turn and the light indicates power in the output cable, the problem is internal to the starter motor. If when it 'clicks' and doesn't turn and the light does not indicate power, then the problem is either in the solenoid or in the connections coming from the battery to the solenoid (but not in the key circuit if I'm using a remote start swithc).

__________________
1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13