Thank you very much for the reply. Not a squeal - more of a rumble/vibration, with maybe a hint of low-frequency squeal in it... As time goes on I'm hearing things (and feeling through the shifter) as I shift other gears (not just initially). It's getting more difficult to get back into first sometimes, so now I'm thinking that it's the transmission - which seems to be what you're suggesting. Noises are more often noticed changing gears (including the noise I initially noticed) - so I think it's a bearing on one of the shafts going out. I had a problem like that on a gremlin I was driving back in the '70's, and my brother just changed a bearing at the end of one of the shafts and it was back on the road. I'm seeing google searches give $2500 for just the rebuilt transmission itself for this pathfinder, so I'm a bit flummoxed on how to proceed! Maybe I could find a used (rather than rebuilt) transmission - although I'm not sure where to go for that nowadays.
EDIT: It looks like it *is* likely the pilot bearing(ish) problem. Now, when I try to downshift to 3rd, I get the noise when I move the shifter-lever toward 3rd (through neutral from 4th, appropriate engine RPM for that), independently of pressing on the clutch. So, it's the transmission, not the clutch. So, I'm wondering if simply replacing bearings is an option (rather than buying a fully-rebuilt). The synchros seem fine.
EDIT2: Now that I have driven it more, the synchros are great, so maybe I should just ask for a new clutch, pilot bearing (or is it a bushing on this car??), and rear main seal. It seems like that would be easier than trying to rebuild the transmission - as I said, the synchros are OK.