If jumping the terminals 1 to 3 always results in an engine start, then it says that any or all of the things bypassed could be the problem. This includes the NSS, the "ignition" electrical switch, and all of the bypassed wiring.

In re-reading the initial post, it says that the minute is the wait time before the starter starts to operate, not that a minute of starter time is required for the engine to fire.

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1961 190Db retired
1968 220D/8 325,000
1983 300D 164,150