Hello RonJ66
I don't have one, but according to those in the know, the Thinlines should sound warmer than a standard Tele if anything.
Couple of things to note.
A. The pickups are alnicos so they'll be naturally brighter than a Tele with ceramics.
B. Default strings are .09s and generics (Fender don't specify other than nickel steel and gauge) which aren't the greatest sounding strings IMPE of them.
Personally I'd stick with .09s initially on that guitar as it has a bone nut set up for .09s. D'Addario EXL 120s or Ernie Ball Super Slinkys are both great sounding and playing strings. Coated strings will generally sound duller, so you could try those for a less bright tone if you prefer. i.e. D'Addario XSE(lectric) 0942 recommended.
See if that makes any difference. If not, try .010s if you want which will eliminate that niggling gauge doubt in your mind. That's your quickest, easiest and other than self-setup, cheapest potential solution after rolling off the tone knob.
If it was my guitar however, after fitting that set of quality .09s as already recommended, if rolling off the tone knob in conjunction with pickup selection doesn't result in the tone your looking for, I'd check a couple of things first before changing string gauge to .10s on those tall narrow frets and bone nut cut for .09s.
Check the action is within specification, which is relevant to pickup to string heights, level and string radii which you should check next. Particularly note the pole to string heights on the bridge pickup and on the high e string you're finding too bright. The bridge pickup is slanted for that very reason and is naturally brighter than the neck because of its proximity to the bridge.
Having done that, select the pickup positions, try all three and see what you think. Adjust the neck pickup height too and level it if you think it needs it. The bridge pickup when selected is supposed to be a brighter and spankier sound.
Still too bright? Roll off the tone knob until you detect it start to cut out the treble and see what you think. That's what it's for.
Still too bright? Time to check the internals. Check the fitted capacitor value and tone pot. The capacitor should be 0.047uF for a warm tone. If it's 0.022uF there's a possible reason your guitar sounds bright. Also check the pot value. 500k will be brighter. If you've got 500k and 0.022uF with Alnicos, there's your potential reason. Change the the capacitor to 0.047uF or swap the tone pot for a 250k or both (or have a luthier do it for you) and see how that plays.
You can change string gauge to .10s, but it won't do a whole lot if the underlying cause lies elsewhere, and .09s will fret better on that neck config IMPO. I have x2 Teles with .10s fitted on different necks with medium jumbos and a Squier Tele with a similar neck and tall narrow frets with .09s.
Have fun & GL.
