Conclusion:　 When you want to say "the rain is coming to a stop". 雨が止みます is appropriate. Neither of 雨が止（や）めます nor　止（と）めます don't mean what you want. -------------------------------------------------------------------- ＊＊＊ 止む（やむ）： 自動詞 stop itself, 　「雨がやむ」 　「雪がやんだ」 　「やむをえず」「やむにやまれず」 -------------------------------------------------------------------- ＊＊＊止める（やめる）： 他動詞　stop something, 「仕事を辞（や）める」 「今日の作業はここまでで、やめよう」 「俺たち、もう、やめにしよう」 -------------------------------------------------------------------- ------------------------------------------------------- **** One question for your sentences,「あめが止めます」 Which did you want to say, 「止めます(とめます）」or 「止めます（やめます）」? These two words, 「止める（とめる）」and 「止める（やめる）」, are so confusing.They shares same kanji and look same (not alike, looking SAME), and mean alike, however they are diffrent words,their pronounciaitons are dfferent, and their meanings are, though similar, but diffrent. - やめる： stop something, stop something/some motion which has continued so far (it would not likely to start again). - とめる：stop something stop something which wants to move more. (it would likely to start again). e.g, - クルマをやめる　： stop driving cars (in daily life) I won't drive cars any more. - クルマをとめる　： pull up and park the car. - 仕事をやめる: quit job. - 仕事をとめる：stop what you/they are doing - 農業をやめる: quit farming - 農業（の発展を）止める：keep agriculture from developing itself +++ For the reason why two words which look alike but are different, share the same kanji -> See. https://www.italki.com/question/424823

止みますneeds subject. 止めますneeds object. 雨が止みます。This Japanese is correct but we dont use it. Because we cannot tell the rain will stop 100percent. Instead, 雨が止みそうだ。雨が止むみたいだ。

The phrase uses the verb 止む (やむ), which is different from 止める or 止まる.