I apologize for being judgemental instead of staying on topic.
About FET testing with a curve tracer:
- a curve tracer would make sense as didactic instruments, or maybe to pair some components, yet it doesn't add much value in the lab for day to day use, IMO. Sure, it can be used to sort out bad transistors, too, but a curve tracer will be an overkill.
- a curve tracer doesn't test leakage. In fact the stairs voltage that will drive the gate will shunt the gate with a much, much less impedance than the gate of any FET.
- the traced curves for FET varies a lot, even for two transistors from the same batch. Also varies a lot with temperature, so they certainly won't look like the ones shown in the datasheet
https://eu.mouser.com/datasheet/2/676/jfet-2n4117-2n4118-2n4119a-interfet.r00-1649084.pdf the datasheet curves are for reference only.
How to measure a FET in general, for no matter what application, might be a difficult task. However, deciding if a FET from an old module is good/bad, would be much easier. Usually semiconductors doesn't wear out, so it would be enough to identify the defective ones. If not defective, measuring its parameters would help at all, since that board was working once.
It's unusual for a FET to be used as a switch and require very high impedance at the same time. Could be, but very unlikely. Very hard to treat all the aspects at the generic level.
To measure pA or fA precisely is far from trivial, but usually the
exact value is not needed. OTOH it's almost trivial to compare the leakage of two FETs, or to detect if a FET is not in specs any more (for example because of some invisible dirt film on the exterior.
Would be even possible to measure those pA/fA gate currents with good resolution, just that the measured value would not be calibrated. To do that just power the DS circuit, for example with a 9V battery and a 100k series resistor, and leave the gate floating in the air. Now if you touch the gate, it's internal capacitance will charge from the hand (or better charge the gate by connecting it to a known voltage then disconnecting the gate), then it will start to slowly discharge because of the leakage. This can be observed as variations in the DS circuit, variations easy to measure with any multimeter. A good FET would take a very long time to self-discharge the Cgs by leakage.
For example, to discharge a 2pF at 250fA (typical input parameters of a 2N4118) would take about 8 seconds for each volt to discharge. Charge Vgs with, say, -5V then disconnect the gate and measure how long until the FET switches off the current through its DS circuit. Not a precise methode, and sometimes it will take way longer than that to discharge the Cgs, but can detect defective or very dirty FETs.
Sometimes this trick can be achieved by simply connecting a multimeter (disable the autorange) between the DS like would measure resistance of DS, then play around with the floating gate. Depending on the multimeter, this might or might not work, better use a voltage source and a resistor, and measure the Vd instead of Rds.
Very hard to consider all the aspects at the generic level. A FET could be as well in a $1 vintage ray-gun toy or in a very sensitive electrometer. If disclosure is possible, what are those boards to be restored? Is there a schematic?