I believe they are electric.  It is not uncommon for one or more
wires to break internally where they connect between the door and the
frame.  The wire may look ok from the outside.

I had to replace 3 of the 4 door lock mechanisms on my 2000 Jetta.
I tried rebuilding one of the lock mechanisms one time just for
kicks and to determine what failed. It seems to be the motor.
Either the brushes wore down, or a winding burned out, because
they would only start from certain rotational positions. There
were also a few dodgy switches in the mechanisms here and there.

The only reliable fix is to replace the modules. You'll need a special
12-point bit to get the latches out of the doors and a couple Torx bits
to get the door apart and (IIRC) a 10mm socket to loosen the window clamp
and remove the glass so you can get the service plate off. There are about
12 bolts around the perimeter of the door access plate. The back doors
are worse than the front doors. You have to remove the triangular part of
the pillar between the fixed and moving windows to make enough room to get
the latch out. Also, the rear windows have holes in them through which a
nylon pin secures them in place. This pin has to be removed by turning a
screw into it and pulling it out.

All in all it's a fairly involved process. I can get the driver's door apart
in about 20 minutes, but I've had a lot of practice at this point. Look on
ebay for the lock modules. That's where I got all of mine as salvage. Expect
to pay about $80 per unit, maybe a little more for the LF one. The Bentley
manual has some pretty good instructions about disassembling the doors, which
you'll absolutely need if you plan to take this on.

...Sean.