I have no references for this except my observasions

If the tool pouch on the cartridge box could not hold it, then the most likely place would to secure it to the waist belt near the cap pouch. A sturdy cotton or leather string would do. I don't think every soldier carried a complete set of tools. The NCOs may have carried a complete set and would have been ready to help any problems on the battle line.

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From the O.R.

Typical tools issued with U.S. issued weapons were...

Screw driver and cone wrench
Wiper
Ball screw
Spring vise
Bullet mold

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David Upton