A few things:
The FTn went to the plastic tip stuff around 4435xxx, serial-wise. So, late 1972 or thereabouts. Leatherette changed at the same time.
With respect to a lens that won't index, take a small screwdriver or paperclip and press down on the tab just behind the coupling pin when it's at the minimum aperture for the lens. Then rotate the aperture ring back to the maximum aperture. That should cause it to index to the proper aperture, instead of sitting at f/1.2 and showing a very erratic meter. Other causes of an erratic meter can be the shutter speed ring shorting out against the metal strip. Seems to be more common on the FT2 and FT3 bodies than the FTn bodies. If the aperture ring causes a smooth movement of the needle, but, if you lightly touch the shutter speed ring and the needle pegs at full-overexposure, it's that problem.
To test for dead cells: one thing you can do is set the ASA to 400, set the shutter speed to 1/60, and the lens to f/8. Leave the lens cap on. Meter needle should remain at the full underexposure position. If it centers, then at least one of the cells has failed. Usually shows up as a cell that looks gray, instead of white with the red etching inside the window of the meter cell.
Since the camera is saying 1/4 second when the shop's FTn is saying 1/250, I'm thinking there's some corrosion, maybe on the wire going up through the body either to the meter movement itself or to the power switch at the advance lever. It's not uncommon to have corrosion that's not visible in the battery box, but in the wiring itself. Had a couple FTn bodies that were like that. Except the meters were completely dead. Battery chambers had some minor corrosion, but cleaned up nicely. Still no power to the meter. Pulled the top and ran a couple wires to the battery itself. Meter worked. So, the wires going down through the casting had corroded internally.
To the OP, it might be best to just buy the shop's body and let them either take the other body in on trade as a parts camera, or use it for parts, if the original seller is unwilling to refund your money. I suspect they would be willing to refund it, since you can prove that the camera is not performing as it should.