Does rapamycin (or CR) reduce scalp oiliness/itchiness?

eg Oily Scalp: Why Does It Itch?

it seems mTOR-driven like acne is

If you are talking about seborrheic dermatitis, it does respond to topical or oral steroids which are anti-inflammatory thus rapamycin could work through its anti-inflammatory/immunosuppressive effect - but that would depend on the dose I suppose