Tool for truss rod adjustment?

Well, it depends...

https://www.squier-talk.com/threads/chinese-truss-rod-size-vs-indonesian.57276/

Likely somewhere between 4 and 5mm. Some say a 3/16" "works".

I have also seen this quote:

"Indonesian and some Chinese use 4mm truss rod adjusters. Some Chinese and all Korean use 5mm truss rod adjusters"

I guess you are on your own. I would advise getting a METRIC set of Allen wrenches (long handle) for about $10. An individual wrench will likely be $5-8. You will probably need them for saddle adjustments as well. Did you get any with the guitar?

Just make sure the wrench fits well. If it fits loosely, you will likely ruin the nut, not the wrench!

Suggestions:

1. Always loosen string tension to adjust. This lessens the likelihood of stripping threads and nuts.

2. Always begin by LOOSENING (counter-clockwise) the nut slightly, paying attention to the position of handle of the wrench. The nut is often "frozen" and it will be easier to unfreeze by loosening. Then return handle to starting point and adjust carefully from there.

3. If there appears to be corrosion and the nut requires allotta force, you may want to take it to a tech to mess it up.

 

Truss rods are just a standard allen wrench head in various sizes. Each brand seems to be a slightly different size.

 

When you say the strings are too high are you looking at neck relief? You need to check that prior to adjusting anything. Most people like a very slight amount of neck relief but some like the neck perfectly flat. On certain Telecasters there is a body route (for base adjustment) to insert the wrench but you have to take off the pickguard to access. It could be straight slots or a hex style, I have both.

 

True for Fender headstock adjust- but could be metric 4mm or 5mm or standard sizes. ... heel adjust is slot or screw usually. Gibson has a tool as it's more like a socket, rickenbacker too.

So there isn't hard and fast rules- just options per instrument and brand.

 

I can only recommend what's worked for me, but this guy's setups are great for Teles and Jags, I assume other models. No affiliation:

https://hazeguitars.com/sketchysetups

 

Truss rod adjustments are not intended to adjust string height. Making changes at the bridge and/or the nut are the proper places for string height adjustments. However, you do need to have neck relief adjusted properly before you start messing with bridge and nut adjustments.

 

I did a little write up about how I approach doing a setup. It is more than just turning a truss rod to lower the action

https://www.tdpri.com/threads/basic-setup.952636/

 

The best one for vintage style is this one available at stew Mac



Oops I didn’t read

You just need some Allen keys probably metric

 

As stated, never adjust your action with the truss rod...it's a totally independent procedure.
First, check if your TR needs adjustment and proceed.
THEN start thinking about action.