Fuse keeps blowing (driver power seat)

So, the driver's power seat stopped working. Checked and found its fuse (20A) blew. Replaced fuse and seat worked just long enough to move it so I could at least fit in to drive, but then blew again. Bought some fuses and replaced it again. This time it was blown before I could even move the seat at all (key not in, seat normally works with out key). Had lots of fuses so tried another. Blown.

Bleh.

So now I've been researching how to track down a short. But I keep getting confused.

First I thought it may have been the power seat switch (because my multimeter's continuity gave different tones when testing the 8-way plug after I removed the switch completely). But a new-ish switch I bought off eBay also behaved exactly the same way on multimeter.

Now I'm trying to use multimeter to narrow down where short is happening.

Question: if I disconnect negative cable from battery, should I get ANY continuity reading at all when testing between the neg/pos holes of a cigarette lighter connector plug? Because I do. Even though it's not full continuity as you get when touching the multimeter's probes together. It's close though.

I couldn't understand why that should happen, so I tried the same test elsewhere. Pulled the light bulb out of the passenger's door, and tested either side of the plug it went in. Same. Seeing continuity with neg cable off battery (pos. Cable still attached).

Shouldn't there be no continuity between neg and pos points on a device plug? Especially if neg. Battery cable is detached.

What to do? Test between power seat switch plug and fuse holes?

Thanks.