I posted in your other thread about the orange and black wires that you found, I think that is your problem with the blower motor, so read that, and do those tests first....
but if here is how to test the brown/purple and black wires that you asked about, I tried to keep the explainations basic and simple, so if you have questions, feel free to ask, or if you already knew something and I'm explaining it overly simplisic, I apologize. I also suck at trying to explain stuff sometimes so tell me if something doesn't make sense
here's another copy of the HVAC schematic that I posted in your other thread. its just easier to have it in front of you while reading this all, and when learning to test electrical systems, you'll want to get familliar with reading schematics like this, if you're not already:
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okay, now looking at the brown wire comes from the 25A HTR-A/C fuse which according to the schematic is hot in run (aka. power is being supplied while the engine is on and running, and assuming the 25A fuse isn't blown)...and runs directly to the HVAC blower control switch, so pull the switch out of your dash and find where the brown wire connects to it. you'll probably have some kind of plug or something you can unplig from the control panel (I've never had my HVAC controls out, so I don't know what it specifically looks like.), but you can unplug it, turn your truck on, and with your DMM, with the black probe first, you'll want to find a grounding point, the actual battery would be ideal, but you probably won't be able to reach that, so find some nice clean bare metal ground point, and hold the black DMM probe tip against it. then use the red probe tip to touch the metal in the connector on the end of the brown wire. now looking at your DMM readout with the dial on the DC voltage setting (the red boxed setting at ~1 o'clock on the dial, I think the symbol shows a capitol V with dashed lines above it), it will show the voltage at that brown wire. this is a direct voltage source so you should be seeing ~12-14V depending on what your charging system is putting out.
to check the purple fan signal wire, you'll need to connect all the blower control switch back together, then unplug the fan connector (with the purple and black wires), and basically you test it the same way. so turn the truck on, turn the blower motor controls on, find a nice bare metal grounding point to use for the black DMM probe, the use the red probe tip to touch the metal connection on the end of the purple wire. it'll read back the voltage at the purple wire. the voltage it reads will be dependant on what setting the blower controls are set at. my estimation would be 3-4V for low speed, 6-7V for med-low speed, 9-10V for med-high speed, and 12-14V for high speed. (this is assuming that the whole blower motor circuit is functional, if the orange wire that you found in the engine compartment is actually the high speed blower motor wire like I think it is, and it's not spliced together, then you will get zero, (or close to zero) volts as a reading from the purple wire on high speed.
the last one you asked about was the black wire. this one is a little more difficult to test. this wire is a gound wire, so there is no voltage running through it unless power is running through the purple wire, AND through your blower motor, AND assuming that the wire is making a good ground connection (I think the black wire in your engine bay is this wire, and by cutting it makes your blower motor non-functional since the circuit cannot be completed (the electrons have no where to go to return to the battery). however, in order to test ground wires like this, you need to have BOTH ends of the wire available. which is difficult since we have one end of the wire that is at the blower motor plug, but the other end is spliced together with other ground wires and is frame or body grounded somewhere else on the vehicle. (the schematic says that its on the right front wheelhouse). so we have some options when testing wires like this, if we actually DO have both ends of the wire handy and available, what you'll do is to set the DMM to the OHM setting (at approx 2 O'clock on the dial, its the white omega symbol), this setting will read electrical RESISTANCE. so with both ends of the wire touch each probe tip to each end of the wire and it'll give you a readout of the OHMs of the wire. the lower the number the better electricity can flow through it. (remember to look at the upper right portion of the readout, it will give you what units it is using, milliohms (indicated by a lowercase m and the omega symbol) is whatever the readout is times 0.001, so milliohms are very small, ohms (just the omega symbol) are just striaght up ohms, no prefix, so whatever the readout is, is what the ohms are. kiloohms (indicated by a lowercase k and the omega symbol) are whatever the readout is times 1000, so kiloohms are large, and lastly, Megaohms (indicated by a capitol M and the omega symbol) are whatever the readout is times 1,000,000 so Megaohms are huge. so when we're testing the resistance of a wire, we want the smallest number possible. if the readout shows zero Megahoms, then that means the resistance is infinite and the wire does not have any electrical path from one probe to the other, this can happen when the wire breaks, or is cut, etc. this can help test if a wire is broken within the insulation where we can't see.
okay, so testing the resistance of a wire which we have both ends is easy like we said, just touch one probe tip to one end of the wire, the other tip to the other end, and read the resistance, if we don't have the second end of the wire (like in the case of grounding wires and what not, we can touch one end to the black (negative) post on the battery. every ground wire should have an electrical pathway back to the battery. this will probably give higher readings since the length of the wire, the quality of the connection for the wire at the frame/body, as well as the quality of the connection for the frame/body to battery. however it should read something, it should never be infinite (zero megaohms on your DMM)
so those are the ways you can test those wires. however I REALLY think those cut wires in the engine bay are the problem. test those first like I talked about in your other thread, then move on to testing these out if the orange and black ones aren't the problem.
