Use 'rearmost' when describing location within a physical space, often in transportation or architecture. The rearmost engine on the airplane is the last one you see before boarding.
Pro Tip 2/3
Relative Position
'Rearmost' shows that something is the last in a series or sequence, not just at the back. My locker is the rearmost, right after Jake's.
Pro Tip 3/3
Not for Time
Don't use 'rearmost' to refer to time. Use it only for spatial positions. Incorrect: He arrived at the rearmost minute. Correct: He arrived at the last minute.