vein (blood, ore), pulse, hope
脉 centers on a channel that carries something essential: a blood vessel, a mineral vein, or the rhythmic pulse of life. The sense of hope is a natural extension of a vital life-line.
脉 is a variant form of 脈. It combines ⺼ (flesh/body part) with 永, which likely contributes a sound element related to branching or flowing. The character originally depicted the branching network of blood vessels.
The left side ⺼ suggests the body, and the right side 永 looks like a branching stream. Picture a network of rivers inside the body carrying life: that is a vein and its pulse.
For ミャク, imagine a tiny cat (みゃあ) mewing as it feels the pulse in its vein: みゃあ -> ミャク, and the pulse beats under the skin.