noun
Refers to a general time, period, or season. Often used in set phrases like この時分 (around this time) or あの時分 (in those days).
この時分はいつも雨が多い。
It always rains a lot around this time of year.
あの時分はまだ若かった。
I was still young in those days.
noun
suitable time; opportunity; chance
Indicates a good or appropriate time to do something. Often used with verbs like 来る or なる to mean 'the time has come'.
そろそろ出発する時分だ。
It's about time to leave.
計画を始めるには今がよい時分だ。
Now is a suitable time to begin the plan.
自分 means 'oneself'. Despite the identical reading, 時分 (じぶん) is a completely different word meaning 'time' or 'season'.
Compound of 時 (じ, 'time') and 分 (ぶん, 'part' or 'portion'). The reading じぶん is a regular on'yomi combination. The word has been used since classical Japanese to refer to a point or period in time.