2001 is an R50. The WD21 ended in '95 in the US. The question is whether you've got the VG33 (3.3l) or VQ35 (3.5l).
Looks like there are two switches on the brake pedal. One for the brake lights, one for the cruise control (which Nissan calls ASCD for some reason). If the R50 pedal assembly is built like the WD21, there's a little rubber plug that bumps against the end of the switch, until it cracks and falls out, and causes the switch to think the brakes are always pressed. Check for that before assuming it's the switch. There's a troubleshooting section for the cruise control in the EL section of the service manual, which you can download for free from Nicoclub. There's an '01 and an '01.5 manual, depending on whether you've got a VG or a VQ.
Cutting the wires at the pumps will not do what you want it to. The front pump is ground-switched (one side of the motor gets fused power, the other side runs through the switch, then to ground), so grounding it at the pump would cause it to run constantly. The two pumps do not share a fuse with each other, though they do share fuses with their respective wiper motors--so if the wipers work, then you know the fuses are OK. If the front wipers work, then you know the ground points for the pumps are OK, because those circuits share the same two ground points.
I would check the pumps first. Unplug them, see if the plugs are corroded, see you've got power and ground at the plugs (while someone holds the washer button). Power the pumps directly with jumpers or a drill battery to see if they go. I would not be surprised if the pumps were seized up, especially if the truck sat for a while (or if the previous owner just didn't use them).
"Wiper and washer" (also in the EL section) has the circuit diagrams for the pumps and wipers. Those diagrams and a voltmeter should be enough to track down where the problem is.