N.B. Derivation of ~まい involves uncertainty - extension to 'negative violition' arrived the same way as the +ve violition did. Therefore, literally, it's more like "I probably won't tell ..." "I don't think I'll tell ..."
What about a past tense? How would one say: "He wouldn't tell me." ?
彼は言わなかっただろう。 I don't think there is a past tense of まい version. 言わないだろう。/ 言わないようにしよう。is more popular spoken style of 言うまい。