Teaching a Feeling is a nice headpat simulator. Slave Maker 3 does have you taking care of various girls much like you'd do in Princess Maker games.
Anyway I'm assuming you mean that the PC can't be the girl you're taking care of since otherwise basically all female protagonist games that aren't visual novels would count but then again you're also asking for any strategy games so who knows.
By strategy like games do you include ones that just have a tactics type battle system(ie. Final Fantasy Tactics or Fire Emblem) such as Futaring or Kamidori or should they be more like XXXivilization?
Nai's Training Diary is similar to Teaching feeling, but can be a lot less wholesome. There's also Imouto!? Life and 1Room, the girls are less reliant on you though. Gran Ende II is rpg, but your caring for a little elf girl.
If you like Teaching Feelings art (and monster girls) you might like Butterfly Affection.
Teaching a Feeling is a nice headpat simulator. Slave Maker 3 does have you taking care of various girls much like you'd do in Princess Maker games.
Anyway I'm assuming you mean that the PC can't be the girl you're taking care of since otherwise basically all female protagonist games that aren't visual novels