Ok, so, Went to figure out the turn signal issue with my recently purchased 2001 Ford Ranger XLT 4.0 4x4. Thought the front right headlight was out and went to change it. Made a discovery. Turns out the turn lights are wired as running lights, running lights are wired as running AND turn, and headlights only turn to high beam if high beam is pressed on but not clicked on, no low beam. WTF did the previous people do!?

 

You need to the HeadLamp\RunningLamp WiringDiagram for your vehicle; RonD on this forum should have a source for that.
Consider a trip to a junkyard or used car lot; compare & take pics of similar Year+Model lamp harness+wiring.
My 2001 SportTracJob2 is a near twin of your 2001 Ranger ExtendedCab+4.0L+4WD.
The ColumnMountedMultiFuncSwitch & the LeftDashMountedLampSwitch are both NotoriousFailureItems,
so could be a combination of issues, in addition to PO making a mess of the wiring.

 

After doing some digging and looking at other videos of rangers, i came to realize Ford made yet another "Advancement"...
On my old 2000, what WAS the corner turn signals are now the Running/Parking Lights, and the Running/Parking lights are now the turn signal. Why the low beams don't work is still a mystery to me, but still working out the bugs on the truck. Previous owners beat the bajeezus out of it.

 

The Flash-to-pass on the multi-function switch has 24/7 12volt power not thru the main light switch, if low and high beams don't work then could be main light switch issue, or fuses

Park lights also run thru main light switch

Turn signals and 4-way flashers share the same Flasher but different fuses, 4-ways have 24/7 12v power, turn signals do not

The front and rear turn bulbs use different wires out of the multifunction switch, try 4-ways first, if all 4 corners work then the wires are OK
If just the front work and not the rear, or visa versa, then could be multi-function switch issue

 

What I've found is that when the switch is turned to Headlight, low beams won't turn on. When I flash high beams, they come on, but when I turn high beams on, they don't turn on. I've even replaced the Multi-switch, still nothing. All fuses have been checked and are in proper working order.

 

Need to study the diagrams RonD provided above, then patiently check one wire, one terminal at a time, looking for shorts, confirming continuity, bad or burnt terminals,, and that PO did not change things around.

 

No need to start by studying a wiring chart. Just start looking for alterations to the existing wiring harnesses. They're most likely out where you can see them.

 

I did find at some point, someone installed a "Viper 5901" Remote start/Etc. system in it. I removed the modules and reconnected any wires that were altered, still nothing. Out of curiosity, would the low beams not working affect the high beams not turning on, but allow you to Flash your high beams? Cause while under the truck, I noticed someone had installed some Xeon modules underneath for Xeon fog lights (Which are broken/missing). I've been tracing around like a madman, even found someone decided to wire in bigger speaker wire to the original smaller speaker wire, as well as mis-wired the driver side mirror (Had to play Guess Who to change the movement from being either reversed or diagonal). I'm getting the feeling it was at some point a kid's "Whip". Tinted headlights and taillights and all.

 

The low and high beams have this power path
Main light switch(on)-----------multi-function switch------------------fuses------------------headlights-----------ground

Flash to pass has this power path
12v power---------------------multi-function switch--------------------fuse-------------------high beams---------ground

So low and high beams need 12v power from main light switch, flash to pass does not

If you have already replaced the multi-function switch then main light switch would be next on the list
Since you already know how to remove multi-function switch you can do that and then test the plug ins for 12volts per wiring diagrams, you will find the flash to pass 12v wire, and you can use that with a jumper wire to power the Low Beam wire and then the High Beam wire
If both work the wiring from there thru the fuses is OK
So main light switch is most likely the issue
But you can test that wire to see if it has 12v with main light switch ON