Bummer - but shit happens...
Anyway, besides the VIA there appear to be only two other circuits that are supposed to drive the synchronous serial data line, these are the real time clock chip and the I/O board. You can disconnect the latter, this shouldn't affect the operation of the main board.
I had a closer look at the "*very* low bit rate signal" and it turned out to be a TTL square wave of exactly one Hz ...
The clock chip (NEC uPD1990) 's output is supposedly open-drain and disabled if OE is low (which it was, or so my oscilloscope indicated). I was about to cut that pin (do I need the clock I wonder again?) when I had a second (or thirteenth) look at the schematic and noticed that the clock chip's OE is driven by the VIA 6522, which I removed, *cough*. A 10-times oscilloscope probe was enough to pull that pin down ...
So back in with the 6522 and indeed the mysterious 1Hz signal is gone.
There is some activity (~100kbps) on the data line of the system-wide serial bus on boot, but the clock signal looks weird (as if it it tries, but would be pulled up hard elsewhere). I bent pin 18 of the 6522 (CB1, which drives the clock of the internal serial bus) carefully out and removed the I/O daughter board and then the clock floats. I need to have a closer look at that I/O daughter board.
(I wonder now, whether, while originally connecting the oscilloscope to the serial data out BNC, I caused the freely dangling I/O board to make contact with the chassis).
With CB1 of the 6522 connected to clock again, that's static at high and there doesn't seem to be any activity on the data line either. I checked the chip select inputs on both ROM chips as well as the 6522 and they are all briefly (~5us) activated after RESET (so at least the CPU and the address decoder seem to work still). If I had one lying around, I'd swap the 6522 with a known good one now. Jameco has (plenty of) the CMOS version from WDC -- are those compatible?
Might be helpful for others (including me, later) attempting to troubleshoot a 705: where R114 and R115 meet, a RESET can be induced safely by pulling that point briefly to GND (the reset button on the front panel won't do any good until the system is mostly functional and can poll buttons).
You may want to check if there's activity on the CPU's address lines, and if so, monitor the outputs of the address decoder (U112) if it still enables EPROM, RAM and the peripherials at a certain pace.
Thanks for the hint, partly done, see above.
The big advantage of circuitry of this age is that things are still quite simple and obvious, and signal speeds don't require special probing techniques or specialized equipment in general. These Keithley "Brownies" are very repairable, though sometimes their analog circuitry is quite intricate - and that's not present in this 705 scanner .
Yeah, the 705 is as easy as one could hope for (earlier devices have so many low density integration chips and discrete parts that they tend to be mechanically challenging and complex to trace, later ones use SMT parts and ASICs/FPGA where repairing generally means replacing unless one has specialized tools and the skill to use those).
I'm sure you'll get it fixed.
Well, I don't want to give up just yet, but the 705 is odd in that it is (currently) *very* affordable on the secondary market, so it doesn't make much sense to spend too much time on that (it's even questionable whether replacing parts is the most economic solution).