The NiChrome won't get the YSZ hot enough to incandesce on its own, but it should get it hot enough (~600°C) to allow the YSZ to start conducting enough that the (resistance to the) flow of current through the YSZ will start raising the temperature further.
If I were attempting this, I try a setup something like this:
View attachment 132862
Heater element consists of 60 turns (around a 2mm former) of 0.5mm NiChrome wire + 20mm & 50mm tails for a total length of 536mm.
(It's intended to slip inside the cruciple.)
The wire has a resistance of 5.551Ohm/M so the resistance of the coil is 2.9786 Ohms. Call it 3 Ohms.
If you put 30V through that you get a current of 10A; and a power disipation of 300W or 300J/s.
The cruciple has a volume of 420.97683694mm³ and the ebay page lists the density as 6.02g/cm³ giving it a mass of 2.5342805583788g, or 0.002534kg.
According to
this pdf YSZ has a specific heat capacity of ~45000 J/Kg*°C. (At 600°C)
45000 * 0.002534 = 114.03J/°C
Which -- ignoring losses -- means the heater element ought to raise the temperature of the cruciple by a bit under 3°C per second.
So around 3 minutes to reach 600°C.
At that point, you'd probably need to switch the heater off and hope that the YSZ will conduct enough to continue raising the temp.