The same Tektronix AM503 current probe amp with the slightly disconnected JFET developed a nasty 120 Hz hum, which can mean only one thing:

Dunno how I missed that while I had the cover off, but there it is. For future reference it’s C165, 47 µF 50 V, with an 8709 date code.
This being a PCB made back in the old days, likely with self-adhesive tape strips, the component pads inside ground and power pours lack thermal isolation decorations.
The solder joints on the bottom side looks better than these, honest:

The new cap is 56 µF 50 F, which seems Close Enough.
The other caps have reasonable ESRs, but I must lay in a stock of high-voltage ‘lytics, as the “new” one is definitely old enough to know better, too.
Now that I check, the amp still produces a very low amplitude 2 MHz sine wave on its 1 mA/div and 2 mA/div settings, suggesting Something Is Not Right™ in the front end, but it works well enough to let me defer that fix until later.