Ok so I spent the afternoon being bad patient #1 and had a look at the 8060A again. It hurt but it was worth it. Firstly the meter was dead again. Hmm. So I replaced the battery clip on it which had been yanked off by the previous owner leaving bare wires. This took 40 bloody minutes including finding all the Metcal bits I'd packed away. Fired it up again, a lot of nope again. After doing a full brush over and inspection the elastomere strip looked like the culprit so I took the display assembly off and cleaned the board and both edges of it. Reassembled it and bam, it works perfectly, at least on DC, ohms, continuity etc. I haven't tested AC yet (waiting for FG to arrive).
Reassembled it and we're good. I like the continuity on this. Top notch!
Not content with stopping here, I know these are prone to leaking and destructive electrolytic capacitors so once my arm is better it's getting recapped and scrubbed to give it hopefully a couple of decades extra.
Total spend so far:
Meter - £18
PP3 clip - £0.54
Capacitors - £3 (incoming)
Edit: this came with the grey carry case and some TL75 style probes. I will clean them up as well later. I think the probe tips have had it so they might get binned. I've got some Pomona ones spare lying around.