Not only to Benzmac (who diagnosed the problem right away), Donald, Mike and every body in this forum. I finally got some free time and replaced the Neutral Safety Switch.
For the benefit of the whole forum I made some observations that may help somebody else with the same problem.
I looked through the archives and found step by step directions from downeyjc who replaced his switch in March 2001 (search: REPLACING NEUTRAL SAFETY SWITCH ON 126 CHASSIS). He has a 1985 300sd but the part number is the same 000 545 49 06. I suspect this part fits most "older" MB's. Check with your parts person/dealer. The only step that was not accurate was step # 4 (he was working from memory, I guess) in which you rotate the white ring clockwise to unlock, counterclockwise to lock the electrical connector.
I have access to a lift, which makes things a lot easier, since there is barely any room to work there. Follow those instructions and you shoul have no problem. The only minor problem I found was the new part did not align right away. TIP: connect the sift lever to the switch and THEN connect the two bolts in place. After that, it went right in.
I hope this can help somebody else.
Good luck!

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J.H.
'86 300E