'97 E250 intermittent won't start/ or even all dead

All of a sudden, my Ford Van would not start: turning the key produced clicking. A battery jump seemed to solve. A few starts later, it wouldn’t start. Battery jump didn’t solve, battery metered at 12.4 clamp to clamp, but shunting the solenoid terminals solved. A few starts later, it wouldn’t start, solenoid shunt failed, battery metered at 12.4 (= alternator OK?), and reattempting key resulted in all dead (dash instrumentation, headlights, dome light, etc.) After a short wait, dash etc., power returned, a key turn = one click sound and all dead again. This pattern held x 3. Then I disconnected the battery, checked fuses in cab and in power distribution box under the hood. None blown. After reinserting them and reconnecting the battery, the van started up as normal; and started as normal the next day (today). What might explain this intersection of all dead, all normal, solenoid shunt works or doesn’t, and permutations? Could a particular fuse have had poor contact that was restored when pulled and reinserted? Note that October = colder and moister re: contacts. Could poor contacts at solenoid or starter motor cause both a failed start and intermittent all dead? What might I try if a later no-start occurs (e.g., clean and emery solenoid and starter motor contacts)?