3/8 fine thread bolts will screw into an 1/8 pipe threaded hole usually. but it isn't a tapered thread and won't seal properly if at all. was the factory plug tapered at all? they do use straight threads for fittings but usually they have an o-ring/jam nut or copper washer to seal the deal. a double male 1/8 inch pipe thread should be easy to find at any atou parts store or you could use a pipe nipple from the local plumbing shop if it is pipe thread. if it's really a staight thread, head to your local hydraulic line repair shop, they should have the oring design fitting. the reason the came up with the o-ring fitting was for aiming the fitting and being able to tighten it pointed in the right direction. some times you can't get a tapered fitting tight when aimed the right way or it won't tighten enough to aim it the right way without breaking it off.
it is possible that the hole wasn't tapped deep enough in the first place with a tapered style, the tap cuts the hole bigger all the way as it is threaded in. that would leave the top of the hole to small. there is a chart that tells how many rotations to screw in a pipe tap for propper engagement. i don't recall the exact number and it is a different number for different size pipe taps.
any good machinist could help you out. if you decide it needs to be threaded further there are ways to do it without getting anything in the hole. shoot me a pm if you decide thats what you need and i will guide you in the right direction.
