"I've checked the fuses, and no power is getting to either side of #6 with the ign on."

That may be a good clue. Despite the fuse cover label, fuse 6 isn't wired to anything on U.S. 240s. But it should have power on the left (input) side, direct from the battery (well almost). Fuses 6 thru 10 are connected to a small, black "Junction Box" on the left front inner fender near the battery.

The power feed into that J-Box is a small red cable that comes from the battery Positive terminal. Sometimes the smaller cable is integrated into that big + terminal, and sometimes it has its own ring terminal on the big one's clamping bolt. The latter type can be loose or corroded, and will also affect the other 3 wires that lead into the car from that little black box.

For safety, disconnect the battery Negative cable, then the Positive one too and inspect that smaller cable for a clean, tight connection. Then scrape clean the inside of the + terminal and the outside of the + post and reconnect it. Do the same for the negative terminal and post.

Then see if your problem is fixed, or if the symptoms have changed.

P.S. you couldn't respond directly to that URL because it was too old and marked "Read Only", where this one says REPLY TO THIS MESSAGE.
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Bruce Young, '93 940-NA (current), 240s (one V8), 140s, 122s, since '63.