Hey there, I've also got a T4900CT, which thankfully came with a hard drive.
The connector itself is a 1mm pitch, 25-way 2 row connector, with a 1.2mm gap between the pins. The part itself seems a bit unavailable as does that type of PCB connector, but here's what it looks like:
Found from checking my connector and doing a search for "Toshiba PCB FX5HD1 P000199390 Satellite 4900CT HDD" but those pictures may fall offline soon so they're attached here.
The maintenance manual says this connector has 60 pins? Well that's wrong 🙁 so maybe we can't just check the maintenance manual - I could help with finding the pinout, but then how to sort the PCB > PCB connector? I'm thinking some 3d printed holder for 2x 1mm spaced FPC cables, going to a custom PCB with the HDD pins on it.