Sounds alarmingly like what my 122 wagon was doing recently, though mine would cut out only for a split second. My cure...well, I started with removing and cleaning the battery to ground connection at the chassis. Then I re-did all the stacked, riveted connections in the fusebox (or you can get one from Ron Kwas).

THe final cure though turned out to be a bad connection at the big post on the starter... since you lose your lights (which are not fused), its gotta be near the main battery connections....

Also check for corrosion in the cables themselves, but my guess is if you remove, clean, and re-attach all them wires at the starter post, your troubles will go away. But clean that ground lead too.

-Matt
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-Matt '70 145s, '65 1800s, '66 122s wagon, others inc. '53 XK120 FHC