Re: New Gold Tone TG10
Standard tenor banjo 1st string (for CGDA tuning) is .09 or .10. The Cafe's article on different mandolin family instruments (link here) shows a .012 for "short scale tenor banjo" GDAE tuning, which would probably be close to tenor guitar scale.
I'd guess .014's a bit heavy. Proof of the pudding is that you keep breaking it. My question is: are you going up from CGDA tuning, that is to tuning the tenor guitar like a mandolin, rather than down, to tuning it like an octave mandolin?
Mandolin scale length's 14 inches, give or take. Tenor guitar's 23 inches, give or take. You can't tune a tenor guitar to mandolin tuning using any gauge of strings of which I can conceive. You can tune it to octave mandolin tuning using strings similar to those of a short-scale tenor or octave mandolin.
As you've deduced, if the string's breaking at a different point, it's probably not a rough spot on the bridge saddle, or a too-tight nut slot that won't let tension distribute evenly over the length of the string. You need a lighter string, or you need to re-think what octave you're tuning it to.
Gibsn: '54 F5 3pt F2 A-N Custm K1 m'cello
Natl Triolian Dobro mando
Victoria b-back Merrill alumnm b-back
Stradolin Vega banjolin
Sobell'dola Washburn b-back'dola
Eastmn: 615'dola 805 m'cello
Flatiron 3K OM