Ruminate is not a specifically negative term in the same way 'delete' is a negative term. It's all in the use and connotation. Bless you, English. I don't know why people insist on getting Japanese kanji and Latinate tattoos when our own language is so damn fascinating.

Pity about the lack of pronunciation, mind. A bit of quick Googling has suggested that it's simply ah-HOYT for pronunciation. My limited knowledge of Germanic derivatives suggests this is probably correct, Americanisation of the pronunciation notwithstanding.