In case you are not aware, later XT's (those with 20MB HDD) had a Xebec controller with a DIP switch block. That controller supported four different drive types.
In every IBM and clone PSU I've ever worked on, the wires from the power connectors are soldered to the same point in the PSU. For example, the +12V wire from each connector is solder to the same +12V point within the PSU.
Therefore if P11 fires up the HDD, then providing that P10 has the same four wires (+12V, GRND, GRND, +5V) then it should also power up the HDD.
If not, there may be a broken wire (rare) or one of the cylindrical metal contacts in the P10 connector has opened up too wide. First, check for a broken wire by measuring the voltages on the P10 connector. You should confirm the continuity of the GRND wires also, and so I suggest the following sequence:
1. Do not plug P10 into anything (IMPORTANT).
2. Connect NEG of multimeter to the PSU case.
3. Connect POS of multimeter to the +12V contact in P10. Multimeter should show +12V. This checks the +12V wire.
4. Connect POS of multimeter to the +5V contact in P10. Multimeter should show +5V. This checks the +5V wire.
5. Whilst leaving the POS of multimeter on the +5V contact in P10, move the NEG of multimeter to the first GRND contact in P10. Multimeter should show +5V. This checks out the first GRND wire.
6. Move the NEG of multimeter to the second GRND contact in P10. Multimeter should show +5V. This checks out the second GRND wire.
If that all measures okay, then I think one (or more) of the cylindrical metal contacts in the P10 plug has opened up too wide. This was a known problem in the days of the XT/AT. Some equipment (eg. FDD, HDD) had pins in their power supply sockets that were either smaller than normal, or larger than normal. If you moved a power plug from a device that used large pins to a device that had smaller pins, instant power related problems appeared.
Widened contacts in the plugs were also caused by repeated insertion/removal of the plugs (particulary if a wiggling motion was used).