How can I tell if my Tele tuning issue is with the string tree or the nut slot?

Sounds like a nut issue to me. I suppose it’s theoretically possible for the string tree to do such a thing, I’ve never experienced it. I’ve known plenty of nuts to need fixing, though. Start with graphite lube, and if that doesn’t work, deal with the nut slot.

 

Nut.
Fix groove.
It's always the nut, isn't it?

 

What string gauge, and if heavier than what Fender fitted, has it had the nut filed?
Forget lubricating it. That's only relevant for guitars with trems, and even then, it's not necessary
As for the string tree, if it's the vintage style, it should NOT be clamped flat to the head. It's there to provide enough angle to stop the strings rattling in the nut. All other style trees Fender has done won't be a problem.

 

I'll respectfully disagree. Any place a string travels over or across (saddle, nut slot, string tree) is a friction point, and a dot of lube goes a long way toward helping keep the strings in tune.

 

Doing?!
Run the point of an X-acto knife or razor blade through the slot, then lube.

 

a common fault.
string bind......rectified by widening the slot a few thou, to accept the strings diameter as it should.

 

Almost certainly a sticky nut

 

Since you may have lubed the nut. Take the string tree off and see if that helps the tuning and go from there. You can also check the winding on the tuners and maybe wind the string down or up to allow more or less break angle.

 

One possible thing it could be is your string jams in the saddle. If you put lubricante it will fix it for a while but it dries you have the same problem. You have to open the slot a bit so the string can move freely

 

Pencil lead.

It will darken a white nut a little, but so does age. You could probably find pencils with a monster truck xxxtreme theme, but it would not be easy.

Also, the suggestion to be sure the nut is cut correctly for your gauge of strings is spot on. It might only need a quick pass with a nut file.

 

Have someone with basic luthier skills look at it. It may need a little filing, especially if you put bigger strings on it. The slipperiest nut lube won't do a lot to fix the issue.

 

string bind=a common factory fault.= improper filing of the slot width[or depth]affects treble strings mostly. simply rectified by re filing slot to correct width/to accept the string[its diameter].allows for transfer of vibrations without hindrance.
the 2 slot walls must not pinch the string too tight etc =cause for string bind. [fuzzy tone]...a jewelers needle file can suffice here..to simultaneously widen the slot/file the 2 walls., but avoid deepening the slot.=fret buzz maybe resulting etc.
a simple diy job rectification .

 

string bind[at the nut]
a sudden drop in pitch when string now fretted., the string de-tunes itself...=string being 'pinched' by the 2 slot walls. when string fretted, it increases the tension momentary! suddenly the strangulated string now releases etc etc=drop in pitch.

 

beeswax

 

Lube is a band-aid. Fixing the nut slot is a far better solution. And yes, you can just take the string tree off as a trouble-shooting measure, but the problem could disappear and still be caused by the nut slot. The string won't be in the same position without the string tree.

Don't use an X-Acto knife. A folded piece of 600-1000 grit sandpaper will do a better job, especially if you pull the high E over to the B string side of the string tree and to the B string's approximate position on the saddle and run the sandpaper under it. That makes sure that the sandpaper "cuts" along the right path, with the appropriate downward angle on the string tree side. Don't overdo it!

 

Nut maintenance is an important part of the setup. Don't be afraid to refine it, just don't scratch your guitar. No, a tiny fraction of a millimeter is not a problem. The danger is going too low. Always fret at the third and check clearance at the first. I also like to use a tuner when I cut slots, but be careful not to go too low. You can use the half pencil method to establish a no-go line, but be sure the pencil is straight and sharp. It's only a guide. The first fret measurement is critical.

 

That would usually be a nut issue. I could see it possibly happening if the tree is way down low with no spacer maybe, but it definitely sounds like the nut slot.

Your nut slot doesn't need to be tight to the string. But it needs to let the string exit toward the body in contact at that edge of the nut.... in a perfect world.