Me too. It's harmless but I've always been curious about this. I have a perfectly functioning 3478A, and I've verified that it is a very real voltage with my antique Keithley 616 connected to it -- the reading matches.
What's funny is that it creeps up to a little over 3 volts, then it sees that it's overrange and it starts toggling between ranges -- and the 616 observes it going between 3 and 0 volts repeatedly. It doesn't need the longer period of time to recharge to 3 volts as when you'd shorted the input. The whole thing is insensitive to the autozero setting too.
If I'm reading the schematic correctly, it looks like there's a 470 pF capacitor in the input circuit which is only switched in for the lower ranges. Where exactly the charge is actually coming from, I don't yet know.
(Edit: and putting the 616 in the 10^-11 amps range, I get about oh, +2 pA out of the 3478A with auto-zero off. With Auto-zero on, it's more like +15 pA)