There are games with resal time and tile-based movement (Age of Empires 1, Warcraft 1), but all those I remember are not single character (à la roguelike).
Do you know any game in which you control a single character that has real-time and tile-based movement?
EDIT: I found one example: Real Time Chess https://www.kfchess.com/
Thanks!
Cataclysm: Dark Days Ahead has an optional semi-realtime mode where enemies take a turn every few seconds if you do nothing, but I believe taking your own turns advances the turn count as usual, so it is really just a sort of (very short) turn timer.
Good one, I forgot about that mode in CDDA!