How much current does this blanket draw (Ampères); or alternatively, how much power does it need (Watts)? And how large are the batteries? (voltage and Ahr)
That'd be important information in suggesting solutions. You could use a resistor, but that would waste half the power from the batteries as heat... and not heat where you want it, i.e. in the blanket. Instead of resistors, you might also use a few lightbulbs... but again, the power would be wasted.
You could use a PWM-type of circuit, something like a TL494 to pulse power so that the blanket sees the correct amount of power (25% on 24V, 75% off, etc.) Might even be as simple as a NE555 with 25% duty cycle and a big FET.
Or you could tap 12V from the batteries; most likely there are two 12V batteries; you could decide to asymmetrically load it, i.e. power it from one battery. Not ideal, but a quick and simple solution. Again, depends on how much power the blanket draws (and how long it's turned on) in relation to the total power consumption of the chair. You might even add a switch to move load from one battery to the other one after a while, so they see more-or-less equal loading.
Or you could try to find a 24V blanket.
Or.... (insert one of plenty of other solutions I forgot to think about)
In my opinion, the most elegant solution would be a small 24V->12V DC-DC PWM converter (NOT a linear regulator; that would waste the excess voltage as heat), using PWM driving a FET. Should be efficient, effective, cheap, relatively simple (though it involves some electronics) and reliable. Such a thing should be not too hard to find in a truck store; truckers have to deal often with wanting to power 12V gadgets from the 24V truck supply. But before you shop for that, you'd need to know how much current the blanket draws.
Oh, just remembered: I once took a small Peltier-fridge/cooling box apart. It could operate on both 12V and 24V. It used a very simple board to convert the 24Vdc to 12Vdc (switchmode, not linear regulation); IIRC, it could supply 4-5A even, which I thought was impressive.
But if you're not good with electronics, and the solution may not cost much, and the load of the blanket is relatively small, then you could try powering the blanket off one (12V) battery.
Edit: or you could get two 12V blankets and wire them in series so they could be supplied from the 24V from the battery. That'd mean all heat would end up where you want it. But it may be too much heat - hard for me to tell, sitting behind a computer screen at the other side of the world....
I'm also reasonably sure that your client isn't the first one to experience that problem. So instead of trying to re-invent a wheel, you might want to try to find out how that problem is usually dealt with by people with that same problem; maybe there's already a very good solution for your exact problem out there....
Edit3: the advantage of a PWM solution would also be that you could make the heating adjustable (in case there isn't a way of adjusting this already on the blanket); by varying pulse-width from 0% to 25%, you could adjust the amount of heat the blanket generates from 0% to 100% of rated power.
