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1/Rtotal = 1/Rpickup + 1/Rpot
So if you measure the total resistance to ground with the pot up full and subtract the resistance of the pot - 1/(1/Rtotal - 1/Rpot) - you get the resistance of the pickup.
If the pot is wired 'backwards' or 'independent' (rotor to pickup), just turn it fully down and you can measure the value directly.
The pot is a little more tricky if it's wired 'conventionally' (rotor to output), but if you realise that when the pot is electrically exactly halfway up, the pot and the pickup are effectively a parallel combination of half their total series resistance, so if you measure the maximum resistance you can get between output and ground, multiply by four, and deduct the pickup resistance you have the pot value.
To get both of them should need to be a process of iteration - feeding the pickup resistance back into the pot resistance calculation and vice versa - or it would be, but the pot resistance is so high compared to the pickup that the difference can safely be ignored.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
The video covers lot of your points!
Measure the resistance from output hot to ground. When the pot is on zero it should read 0 ohms. When the pot is on 10 it will read the resistance of the pickup (or very close). In between, it will rise to a peak - turn the pot back and forth slowly until you find the maximum value. Multiply that number by four, and subtract the resistance of the pickup.
If you want to be very fussy, use the resistance of the pot to recalculate the resistance of the pickup and subtract that instead, but you’ll find it barely makes any difference to what you then get for the pot.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein
One thing that’s worth mentioning - if you do this a lot, or you want to make things easier for yourself, its very handy to have a pair of multimeter leads connected permanently to a guitar jack plug, so you can just plug it in and leave both hands free.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Only two things are infinite - the universe, and human stupidity. And I'm not sure about the universe." - Albert Einstein