"I found a junked HP Laserjet II which initially jammed pulling in the paper. I have fixed that. It still jams on the output, though. It prints nicely, so it seems worth fixing. If I open the back tray, the sheet exits 90% before stopping with the "paper jam" error. With that tray closed, I get the accordion paper jam in the fuser area. I do not detect any rotation of the upper rollers to feed the paper out of the top. When opened, I can roll them by hand easily. I see no obvious gear wear or broken teeth. I also see deep scratches in the grey fuser, which is probably unrelated. The toner does not have any fusing problem that I see in a band down the page."
(From: Tony Duell (firstname.lastname@example.org).)
I think you've got 2 problems here - the false paper jam with the tray open, and a problem with the drive to the top rollers.
Let's look a them in that order.
There's only one paper sensor in the SX engine that I know about, and that's part of the fuser. On the PCB at the left side of the fuser there's a slotted opto-switch with a lever that detects paper in the fuser. There's also a single transistor on said PCB that buffers/amplifies the output from the opto-switch, Q332, I think. This sensor must change state one way (to indicate paper has got to the fuser) shortly after the registration clutch operates and then change state the other way when the paper has got out of the fuser.
You might start by reseating the cable at J206 of the DC controller board (just in case it's bad connections) and then look at the sensor (mechanically and electrically) on the fuser PCB.
Silly question: If the paper tray switches (on the DC controller board) aren't operating properly, could the printer think it was feeding a shorter piece of paper than it actually has, and then give a paper jam error? It's always possible... Alas I don't know the coding for these 3 switches (SW201-SW203)
The other problem is almost certainly mechanical. Look at the gears on the right hand side of the fuser (stripped teeth do occur here) and in the top cover of the printer. Shouldn't be too hard to find where the drive has failed. I suppose you could remove the outer casing and AC block, re-insert the fuser and close the cover, and look at things while turning the machine by hand.